Method and apparatus for the filtration of biological solutions

ABSTRACT

A system, method and device are disclosed for bio-processing a feed stream and providing a constant output by operating a continuous single-pass tangential-flow process. The single-pass process provides high conversion concentration while operating at relatively low feed flow rates, and the process can also be used to provide constant output diafiltration.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/755,009, filed Dec. 29, 2005, and U.S. Provisional Application No.60/754,813, filed Dec. 29, 2005, which applications are herebyincorporated herein by reference in their entirety.

STATEMENTS REGARDING FEDERALLY SPONSORED RESEARCH

Not applicable.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to a membrane separation systems,modules and methods and more specifically to single-pass tangential flowfiltration operation for concentration and diafiltration of feedstreams.

2. Description of the Related Art

Ultrafiltration (UF) and microfiltration (MF) membranes have becomeessential to the separation and purification in the manufacture ofbiomolecules. Biomolecular manufacturing, regardless of its scale,generally employs one or more steps using filtration. The attractivenessof these membrane separations rests on several features including, forexample, high separation power, and simplicity, requiring only theapplication of pressure differentials between feed and permeate. Thissimple and reliable one-stage filtering of the sample into two fractionsmakes membrane separation a valuable approach to separation andpurification.

In one class of membrane separations, the species of interest is thatwhich is retained by the membrane, in which case the objective of theseparation is typically to remove smaller contaminants, to concentratethe solution, or to affect a buffer exchange using diafiltration. Inanother class of membrane separations, the species of interest is thatwhich permeates through the filter, and the objective is typically toremove larger contaminants. In MF, the retained species are generallyparticulates, organelles, bacteria or other microorganisms, while thosethat permeate are proteins, colloids, peptides, small molecules andions. In UF the retained species are typically proteins and, in general,macromolecules, while those that permeate are peptides, ions and, ingeneral, small molecules.

Permeation flux, also referred to as flux, is the flow of a solutionthrough a filter. The ability to maintain a reasonably high flux isessential in the membrane separation filtration process. Low flux canresult in long filtration times or require large filter assemblies,resulting in increased cost and large hold-up volumes retained in themodules and associated filter system equipment. The filtration processitself induces the creation of a highly concentrated layer of theretained species on the surface of the membrane, a phenomenon referredto as “concentration polarization,” which reduces the flux from initialmembrane conditions. In the absence of counter measures, theaccumulation of retained particles or solutes on the surface of themembrane results in decreased flux and if not corrected the filteringprocess ceases to function efficiently. One conventional approach toovercoming the effects of concentration polarization in the practice ofmicrofiltration and ultrafiltration is to operate the separation processin tangential flow filtration (TFF) mode.

TFF filters, modules and systems include devices having flow channelsformed by membranes through which the feed stream flows tangentially tothe surface of the membrane. The tangential flow induces a sweepingaction that removes the retained species and prevents accumulation,thereby maintaining a high and stable flux. Because higher tangentialvelocities produce higher fluxes, the conventional practice of TFFrequires the use of high velocities in the flow channels, which in turnresult in very high feed rates. These high feed rates result in lowconversion, typically less than 10% and often less than 5%. Lowconversion means that the bulk of the feed stream exits the module asretentate in a first pass without being materially concentrated in theretained solutes. Since many UF separations require high concentrationfactors, as high as 99%, the retentate is typically recirculated back tothe inlet of that module for further processing. Systems withrecirculation loops are complicated by the requirement of additionalpiping, storage, heat exchangers, valves, sensors and controlinstrumentation. Additionally, these systems are operated in batch moderesulting in undesirable effects, including subjecting the feed solutionto processing conditions for a long time, often several hours.

A conventional recirculation TFF process including a recirculation loopis shown in the process and instrument (P&I) diagram of FIG. 1. A TFFmodule 1 having a feed port 9, a retentate port 12 and a permeate port10 receives a feed stream 7 from a batch tank 22 through a recirculationpump 6. Conventional TFF processes use commercially available TFFmodules with flow channels of constant cross-section independent ofwhere along the length of the channel the cross-section is measured. Afeed compartment 2 is pressurized by the combined action of a pump 6 andbackpressure valve 15 downstream of the retentate port 12. Pressuresensors 8 and 13 monitor the feed and retentate pressures, respectively.A permeate compartment 3 typically at or close to atmospheric pressureproduces a permeate stream 11 from the permeate port 10 for furtherdownstream processing or storage. A retentate stream 14 returns to thebatch tank 22 through a heat exchanger 16. The heat exchanger 16 isoften necessary to cool-down the retentate stream 14, which can heat upas a result of the pressure energy dissipated through, the backpressurevalve 15. Although the temperature increase across the backpressurevalve 15 is typically only about 1° F., the cumulative effect ofrecirculation can gradually increase the temperature of the batch byabout 10 to 30° F. in the absence of an effective heat exchanger. Tocontrol the temperature of the batch, a temperature sensor 5 can be usedto send a control signal 17 to a temperature controller 18, which inturn can automatically operate a flow control valve 19. The valve 19controls the flow of cooling water 20 through the heat exchanger 16.Spent cooling water 21 returns to a central water chilling system (notshown). To control this process the flow rate of the feed pump 6 can beset according to the module supplier's recommendations followed bythrottling retentate valve 15 until the desired feed pressure isobtained. Typically, these two process components need to be repeatedlyadjusted to account for the increased viscosity of the feed stream 7 asthe feed stream concentration increases as the separation progresses.

These conventional TFF processes possessing recirculation loopstypically utilize flow rates greater than 4 liters/min/m², and moretypically less than 20 liters/min/m². These high flow rates aretypically necessary to obtain practical fluxes and result in lowsingle-pass conversion, f, typically between 5 and 10%. This in turn canrequire that the recirculation pump 6 be very large and the pipescarrying the feed stream 7 and the pipes carrying the retentate stream14 have a flow capacity 10-20 times larger than those carrying thepermeate stream 11. The need for a heat exchanger 16 and associatedinstrumentation, large recirculation pump 6, and large-capacity feed andretentate pipes makes conventional TFF systems with recirculation loopscomplex and costly. Additionally, the large capacity of therecirculation loop can result in a large system hold-up volume (i.e. avolume which remains in the system when processing is complete). Thehold-up volume is a factor that typically leads to yield losses and thatlimits the maximum concentration factor achievable with such systems.Finally, because the process shown in FIG. 1 is inherently a batchprocess it takes several hours to process the volume in the feed stream7 from the batch tank 22 before the desired output is ready for furtherprocessing. As a result, the solution being separated is exposed to theprocess for a long time, which can be a particularly undesirable featurefor sensitive solutions. Furthermore, in these conventional processesthe operating conditions are typically repeatedly adjusted as theprocess progresses to accommodate the changing volume of the batch andthe increase in viscosity that can result from the increasedconcentration of the feed solution.

Several attempts have been made to improve conventional TFF moduleperformance by modifying flow channel topology. U.S. Pat. No. 4,839,037,Bertelsen et al., discloses a spiral wound module with a tapered channelfor the purpose of maintaining relatively constant velocities. U.S. Pat.No. 4,855,058, Holland et al., discloses maintaining flow velocitiesconstant as material permeates, as applied to spiral wound membranes;using reverse osmosis, ultrafiltration and micro filtration membranes,and it describes the control of flow velocities by changing the channelheight, the channel width and the channel length. U.S. Pat. No.6,926,833, and related U.S. Pat. Nos. 5,256,294, 5,490,937, 6,054,051,6,221,249, 6,387,270, 6,555,006, all issued to van Reis, and U.S. Pat.App. Pub. Nos. 2002/0108907 and 2003/0178367, van Reis, discloseimproving the selectivity of ultrafiltration, including maintaining aconstant TMP along the channel length by establishing a tangential flowof the fluid media over a second surface of the membrane and usingconverging channels having decreasing cross-sectional area. U.S. Pat.No. 6,312,591, Vassarotti, et al., discloses a filtration cell forcarrying out a tangential flow filtration of a sample liquid feeding aflow of sample liquid tangentially over the membranes such that eachchannel is connected in parallel. Each channel includes in itslongitudinal direction a number of subsequent channel sections separatedby transitional zones and is constructed and arranged such that the mainflow direction in subsequent sections changes abruptly in thetransitional zones. The cell operates using a conventional TFF processand recirculates the sample liquid through a loop.

In conventional membrane processes such as reverse osmosis, gaspermeation and ultrafiltration the desired separation can be enhanced orits costs reduced by staging. Systems with permeate staging devicesprocess the permeate from a membrane module or a number of modules intoanother membrane stage or module, as the feed stream of this secondstage. This is generally done to further remove impurities from thepermeate. In some gas separation processes both the permeate and theretentate from a module or series of modules is further processed in oneor more membrane stages. Typical of these processes is that described inU.S. Pat. No. 5,383,957, Barbe, et al., which discloses producing purenitrogen from air.

Retentate staging is used in both ultrafiltration and reverse osmosisprocesses practiced on a large scale. In retentate staging the retentatefrom a stage serves as a feed to the next stage. Typical reverse osmosisprocesses include two to four retentate stages. The transition betweenstages is typically defined by a change in total flow cross-section ofthe flow channels in each stage. Typically each stage contains three tosix spiral wound modules in a vessel. In reverse osmosis it is usual forthe overall process to permeate between 50% and 75% of the feed. Inorder to maintain a fairly uniform flow rate through the membranemodules, the number of modules in each stage is reduced to compensatefor the reduced feed rate to that stage. This configuration is known inthe art as a “Christmas tree” design. In ultrafiltration systems,feed-and-bleed stages are used. In this design the effluent from eachstage is partly recirculated to the feed of the stage by means of arecirculation pump. These conventional reverse osmosis multi-stagesystems generally do not exceed four stages because of the requirementfor additional external piping, instrumentation, controls and pumps. Theefforts to apply retentate staging to UF systems based on the usefeed-and-bleed systems have been generally unsuccessful forbio-processing applications. These retentate staged systems usecirculation pumps in each stage, and while they are used extensively inthe food industry for very large scale processes, these systems are toocomplex for use in the pharmaceutical industry and too difficult tovalidate for compliance with regulatory requirements. Retentate stagedsystems are used for water purification by reverse osmosis. Almostuniversally these systems use spiral wound modules. Because of the lowpermeability of RO membranes, thick flow channels are used withoutreducing fluxes materially. Because the fluxes are low very long stagesare needed to achieve a reasonable concentration factor per stage.

Attempts have been made to develop single-pass TFF processes, howeverthese attempts often require very high pressures, a multiplicity of verylong modules in series and with the use of circulation pumps orre-pressurization pumps between stages. The modules usually havechannels with relatively large channel dimensions. These conventionalattempts result in large hold-up volumes and the additional complexityof intermediate pumps, tanks, valves, and instrumentation. In additionto concentration, staged filtration processes are used to carry outdiafiltration. The most common form of diafiltration in continuousprocesses is the “parallel” diafiltration in which diafiltrate is addedto each stage. Counter current diafiltration is sometimes used to reducediafiltrate requirements. In counter current diafiltration freshdiafiltrate is added to the last stage and permeate of each stage servesas diafiltrate to the preceding stage. In both these forms of stageddiafiltration process the total amount of diafiltrate required toachieve a given degree of permeating impurity removal decreases as thetotal membrane area is subdivided into a larger number of stages. Thelimit on the number of stages used is the increased cost as the totalmembrane area is divided into smaller stages. Conventional diafiltrationsystems generally use recirculation pumps with diafiltrate injected justbefore the pumps and do not operate as a single-pass TFF process.

Thus, the need still exists for a simple tangential flow process suitedfor the needs of pharmaceutical and biotech processes which is able toyield high reliable flux and high conversion without the need ofrecirculation loops and intermediate pumps, and that can be readilydriven by the low-pressure differentials between the feed and thepermeate. It would be desirable to operate a bio-processing separationin a single pass mode without a recirculation loop while providing ahigh conversion with a relatively low hold up volume. It would befurther desirable to operate the separation without the requirement of ahigh capacity feed pump and associated system interconnections.Operation of a diafiltration process in a single pass mode would also bedesirable. It would also be desirable to reduce bio-processing systemcost by reducing some of the system complexity by using more versatileseparation modules.

SUMMARY OF THE INVENTION

In accordance with one aspect of the present invention, a filtrationsystem includes a plurality of stages, each stage having a plurality ofchannels providing at least one serial flow path. Each stage is in fluidcommunication with each adjacent stage preceding it and is in fluidcommunication with each adjacent stage that follows it. Each of thechannels includes a filtration membrane and has a length, a membranearea, a void volume, a specific membrane area expressed as a ratio ofthe membrane area to the void volume, and a dimensionless lengthexpressed as a product of the channel length and the specific membranearea. The dimensionless length of a stage is the sum of thedimensionless lengths of each channel in the longest serial flow path inthe stage and the dimensionless length of the system is the sum of thedimensionless lengths of the stages. The specific membrane area of atleast one channel in this system is greater than about 40 cm⁻¹ and thedimensionless length of the system is greater than about 2,000 and thedimensionless length of at least one of the of stages is less than about6,000. Such a system, either internally or externally staged, is capableof operating efficiently in single pass mode and therefore eliminatesthe requirement of a recirculation loop and feed tank, and reduces feedpump size resulting in lower system costs, and a smaller equipmentfootprint. The system can also be scaled in a linear fashion to providefluid stream processing over a wide range of feed volumes.

In accordance with a further aspect of the invention an internallystaged filtration system includes a housing and stages within thehousing. Each stage has a number of channels which are formed by afiltration membrane, and each stage is in fluid communication with eachadjacent stage preceding it and is in fluid communication with eachadjacent stage that follows it. At least two stages are fluidly coupledto form a serial flow path, and there is a change in a filtrationproperty between the two stages in order to maintain separationperformance. Such a system is able to yield high reliable flux and highconversion without the need of recirculation loops and intermediatepumps.

In accordance with still another aspect of the invention, a separationmodule for the filtration of liquids includes a housing, and at leastone hollow fiber membrane which has a hydraulic permeability greaterthan about 2 lmh/psi. The hollow fiber is inside the housing and forms aflow channel. The flow channel has a membrane area, a void volume, alength, a specific membrane area expressed as a ratio of the membranearea to the void volume and a dimensionless length. The dimensionlesslength of the hollow fiber filtration membrane is greater than about10,000, and the specific membrane area is greater than about 50 cm⁻¹.Such a device provides a simple, easily manufactured hollow fiber devicecapable of operating in single-pass TFF filtration (SPF) mode.

In accordance with still another aspect of the invention, a filtermodule for filtering a fluid mixture includes a housing, a membranewithin the housing having a first surface, a feed spacer adjacent thefirst surface of the membrane. The spacer and the membrane form at leastone channel, which is able to receive a tangential flow of fluid overthe first surface of the membrane. The channel has a membrane area, avoid volume, a length and a specific membrane area expressed as a ratioof the membrane area to the void volume and a dimensionless lengthexpressed as a product of the channel length and the specific membranearea. The filter's specific membrane area is greater than about 40 cm⁻¹,the dimensionless length of the at least one channel is greater thanabout 3,000, and the at least one channel having a width generallydecreasing in the direction of the tangential flow. This module is amore versatile separation module and reduces bio-processing system costby reducing some of the system complexity. Such a module facilitatesoperation in a single pass mode without a recirculation loop whileproviding a high conversion with a relatively low hold up volume.

In one embodiment an internally staged filter module includes a housing,a plurality of stages within the housing. Each stage has channels with afiltration membrane and at least one manifold in fluid communicationwith the channels. Each stage is in fluid communication with eachadjacent stage preceding it and is in fluid communication with eachadjacent stage that follows it. At least one diafiltration distributorin the housing is in fluid communication with the manifold of selectedstages and has an inlet for supplying a diafiltrate. Such a moduleallows a diafiltration process to operate with the advantages ofoperating in SPF mode.

In accordance with a further aspect of the invention a single passfilter system includes a top plate with a feed port stacked togetherwith a set of cassettes. Each of the cassettes has a feed manifold, aretentate manifold, at least one permeate channel and at least one flowchannel fluidly coupled to the feed manifold and to the retentatemanifold, the flow channels of the plurality of cassettes fluidlycoupled in parallel. A staging plate is stacked between the first set ofcassettes and a second cassette which also has a feed manifold. Thestaging plate fluidly couples the retentate manifold of one of thecassettes of the first set of cassettes to the feed manifold of thesecond cassette and blocks the flow from the feed manifold of one of thecassettes of the first plurality of cassettes, thereby serializing theretentate flow. The second cassette has a retentate manifold. The systemalso includes a bottom plate in the stack with a retentate port in fluidcommunication with the flow channel of the second cassette. Such asystem permits the use of conventional cassettes to be operated in anSPF mode by serializing at least one parallel flow path with anotherflow path and reduces the need for revalidation of the cassette andsystem performance.

In accordance with another aspect of the invention a method forfiltering a liquid feed includes the steps of continuously supplying thefeed stream into a membrane separation module at a specific feed flowrate of less than about 200 lmh and having at least one channel havingspecific membrane area greater than about 40 cm⁻¹ and operating theseparation module in a single pass tangential flow filtration (SPF)mode. With such a technique used for concentration, highly concentratedoutput is available without waiting for the completion of a batchprocess. Other advantages of SPF operation include reduced complexity,shorter exposure time resulting in less protein damage, highconcentration factors, lower hold-up volume, and reliable control of theprocess. SPF diafiltration provides similar advantages. In anotheraspect of the invention, the method further includes controlling thetransmembrane pressure in the stages of a multi-stage systems and moduleindependently of the feed pressure in the stages by using a permeatedistributor to control permeate pressure.

In accordance with another aspect of the invention a method forprocessing a solute in a feed stream includes the steps of operating aplurality of stages having at least one stage comprising a plurality ofsubstantially identical, long thin channels comprising the filtrationmembrane, in an SPF mode, maintaining separation performance in at leastone of the plurality of stages by changing at least one property of atleast one stage relative to a preceding stage, and continuouslysupplying the feed stream at a low specific feed flow rate. With such atechnique, filtration membranes are efficiently used while achieving ahigh conversion factor and reducing system requirements, hold-up volumeand processing time.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other aspects, embodiments, objects, features andadvantages of the present teachings can be more fully understood fromthe following description in conjunction with the accompanying drawings.In the drawings, like reference characters generally refer to likefeatures and structural elements throughout the various figures. Thedrawings are not necessarily to scale, emphasis instead being placedupon illustrating the principles of the present teachings. The followingdrawings are illustrative of embodiments of the invention and are notmeant to limit the scope of the invention as encompassed by the claims.

FIG. 1 shows a P&I diagram of prior art TFF process using arecirculation loop;

FIG. 2 shows a P&I diagram of an SPF process according to the invention;

FIG. 3 shows a P&I diagram of a an SPF similar to the process of FIG. 2in which two pressurized tanks drive and control the process;

FIGS. 4A and 4B show P&I diagrams of an SPF processes according tovarious embodiments of the present invention in which two pumps are usedto drive and control the process;

FIG. 5 is a schematic diagram of a longitudinal section of a flowchannel of a hollow fiber module formed with hollow fiber membranesaccording to the invention;

FIG. 6 is a schematic diagram of a longitudinal section of flow channelof a flat-sheet module formed with flat-sheet membranes according to theinvention;

FIG. 7A is a schematic block diagram of a multi-stage system accordingto the invention;

FIGS. 7B and 7C are schematic diagrams of internally-staged modulesaccording to the invention wherein staging is accomplished by reducingthe number of flow channels in each stage along the flow path;

FIG. 7D is a schematic diagram of a multi-stage system having stageswith multiple serial flow paths according to the invention;

FIG. 8A is a perspective diagram of a multi-stage system according tothe invention having stages including channels with differing specificmembrane area;

FIGS. 8B and 8C are schematic diagrams of internally-staged modulesaccording to various embodiments of the present invention, where stagingis accomplished by increasing the specific membrane area of channels ineach stage along the flow path;

FIGS. 9A and 9B are schematic diagrams of feed and permeatecompartments, respectively, of an internally-staged module comprisingrectangular channels having decreasing cross-sectional area along theflow path according to the invention;

FIG. 10A is a schematic diagram of a single-leaf spirally-wound moduleaccording to the invention;

FIGS. 10B, 10C, 10D and 10E show multiple views of the spiral module ofFIG. 10A including rectangular channels having decreasingcross-sectional area along the flow path;

FIG. 11A is a schematic diagram of an exemplary staging plate andcassette system according to the invention;

FIG. 11B is a schematic diagram of a staging plate assembly using thecomponents of FIG. 11A;

FIG. 11C is a schematic diagram of conventional cassette as used in thesystem of FIG. 11A;

FIG. 11D is a flow schematic of one embodiment of a single passfiltration concentration module in a 3-2-1-1 configuration according tothe invention;

FIG. 12 is an exemplary flux profile for a concentration module similarto the module of FIG. 11A;

FIG. 13A is a schematic diagram of an internally staged diafiltrationsystem suitable for diafiltration according to the invention;

FIG. 13B is a schematic diagram of one embodiment of the system of FIG.13A, including diafiltration hydraulic distributors;

FIG. 14A is a schematic diagram of a diafiltration distributor similarto the distributor in the system of FIG. 13B implemented as a parallelresistance network of hydraulic resistors;

FIG. 14B is a schematic diagram of a diafiltration distributor similarto the distributor in the system of FIG. 13B implemented as a seriesresistance network of hydraulic resistors;

FIG. 14C is a schematic diagram of a diafiltration distributor similarto the distributor in the system of FIG. 13B implemented as aseries-parallel resistance network of hydraulic resistors;

FIG. 15 is a schematic diagram of a counter current diafiltration moduleaccording to the invention showing the distributors as a parallelnetwork of resistors coupled to a pump;

FIG. 16A is a schematic diagram of internally staged hollow fiber moduleaccording to the invention;

FIG. 16B is a schematic cross section diagram of the internally stagedhollow fiber module of FIG. 16A;

FIG. 17 is a schematic cross section diagram of an internally stagedhollow fiber module suitable for diafiltration according to theinvention;

FIG. 18A is a longitudinal cross section view of an internally stagedhollow fiber module suitable for diafiltration according to theinvention;

FIG. 18B is an axial cross section view of the internally staged hollowfiber module of FIG. 18A through line 18B;

FIG. 19A is schematic diagram of an internally staged module including astaging plate suitable for cross current diafiltration according to theinvention;

FIG. 19B is a flow diagram showing the feed stream in the four-stagemodule of FIG. 19A;

FIG. 20 is a schematic diagram of a staged module suitable for countercurrent diafiltration according to the invention; and

FIG. 21 is a schematic diagram of permeate distributor according to theinvention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to the separation and purification ofsubstances by membrane filtration, and more specifically, to SPFprocesses and devices. The devices and methods of the present inventionutilize filtration membranes to separate components in a feed stream ina single pass at high conversion rates, in which a first driving force,transchannel pressure (TCP), is applied to drive liquid flowtangentially along the surface of the membrane, and a secondindependently controlled driving force, transmembrane pressure (TMP),drives the permeation through the membrane. As these are pressure-drivenseparations, the ultimate driving forces are pressure differentials.Suitable sources to induce the necessary pressure differentials include,but are not limited to, compressed gases, vacuum sources, pumps, andcombinations thereof. The present invention matches these driving forcesto devices having one or more of: a sufficiently large ratio of membranearea to flow channel void volume; ranges of channel lengths, permeatecontrols, and stage boundary transitions in multi-stage systems to alloweffective operation in a single pass of the feed stream through thedevice. The use of thin channels results in high fluxes. The use of longflow paths in combination with selected driving forces provides forsufficiently long residence times in the flow channels resulting in highconversion and efficient diafiltration. The present invention depends,in part, upon the discovery that, when operating in a single pass modeusing long, thin channels and low specific feed flow rates, the fluxperformance of the membrane is not degraded.

Before describing the invention, it may be helpful to an understandingthereof to set forth definitions of certain terms to be used herein. Theterm “separation” generally refers to the act of separating the feedsample into two streams, a permeate stream and a retentate stream. Theterms “feed” and “feed stream” refer to the solution being fed to thefiltration module for separation. The terms “permeate” and “permeatestream” refer to that portion of the feed that has permeated through themembrane. The terms “retentate” and “retentate stream” refer to theportion of the solution that has been retained by the membrane, and theretentate is the stream enriched in a retained species.

The expressions “flow channel” and “channel” are herein usedsynonymously to denote the separation channel comprising a membrane andin which the solution being separated is flowing in a tangential flowfashion. In certain embodiments, the separation channel comprises wallsthat are formed at least in part from an ultrafiltration membrane and inother embodiments from a microfiltration membrane. While channels canhave an axis defined by the direction of the flow of liquid at any pointof the channel, it should be understood that this does not require thatthe channels be straight. Channels can be straight, coiled, arranged inzigzag fashion, and in general can have any topology which supportstangential flow. Channels can be open, as in an example of channelsformed by hollow fiber membranes, or they can have flow obstructions, asin the case, for example, of rectangular channels formed by flat-sheetmembranes spaced apart by woven or non-woven spacers.

The expressions “single-pass conversion,” “conversion per pass” andconversion are used herein to denote the fraction of the feed volumethat permeates through the membrane in a single pass through the flowchannels, expressed as a percentage of the feed stream volume. The terms“single pass concentration factor” and “concentration factor” as usedherein describe the degree of concentration achieved for a specificspecies of interest as a result of a single pass through the flowchannels. The concentration factor is a dimensionless quantity andexpressed as the ratio of the concentration of the retained species inthe retentate to that of the retained species in the feed. Theconcentration factor is also expressed as the volume of the feed dividedby the volume of the retentate where the retained species is almostcompletely retained.

The expressions “liquid velocity” and “velocity” are herein usedsynonymously and refer to the velocity of the liquid within the channelin the direction of the flow path averaged across the channelcross-section. This definition recognizes that, in any flow channel, thevelocity of the liquid is zero at any solid surface and increases awayfrom a solid surface. The expressions “entrance velocity” and “inletvelocity” are herein used to refer to the velocity of the liquid at theentrance of a channel. The term “recovery” is used to denote the massfraction of the species of interest recovered in the fraction ofinterest (permeate or retentate) expressed as a percentage of the masscontained in the feed stream. The terms “volumetric flux,” “permeationflux” and “flux,” designated by the symbol J, are used to describe therate of permeation of the solution through the membrane, expressedherein with the units of liters per hour per m² of membrane area andabbreviated as “lmh.”

The expressions “specific membrane area of the flow channel,” “specificmembrane area of the channel,” and “specific membrane area,” designatedby the symbol σ_(c), are herein used to denote the amount of membranearea contained in a channel per unit channel void volume. Expressed inunits of cm⁻¹, σ_(c) is defined by the following equation:

$\begin{matrix}{\sigma_{c} = {\frac{{Membrane}\mspace{14mu} {Area}\mspace{14mu} {of}\mspace{14mu} {Flow}\mspace{14mu} {{Channel}\mspace{14mu}\lbrack {cm}^{2} \rbrack}}{{Void}\mspace{14mu} {Volume}\mspace{14mu} {of}\mspace{14mu} {Flow}\mspace{14mu} {{Channel}\mspace{14mu}\lbrack {cm}^{3} \rbrack}}.}} & (1)\end{matrix}$

In a multi-stage system, σ_(c) for a stage is represented by the σ_(c)of the channel having the largest σ_(c) in that stage, and generally thechannels in a stage have substantially equal values of σ_(c).

The expressions “specific feed flow rate” and “specific feed rate”designated by the symbol F, are herein used synonymously to describe theflow rate of the feed stream divided by the membrane area of the module.F is expressed in units of lmh as follows:

$\begin{matrix}{F = {\frac{{Module}\mspace{14mu} {Feed}\mspace{14mu} {Flow}\mspace{14mu} {Rate}\mspace{14mu} \lfloor \frac{liters}{hr} \rfloor}{{Module}\mspace{14mu} {Membrane}\mspace{14mu} {{Area}\lbrack m^{2} \rbrack}}.}} & (2)\end{matrix}$

The expressions “transmembrane pressure differential,” “transmembranepressure” and (TMP)” are herein used synonymously to describe theaverage pressure differential between the flow channel, and the permeatecompartment, and given by:

TMP═P _(F) —P _(P).  (3)

Where P_(F)=average of the pressure at the inlet and the outlet of theflow channel; and P_(P)=pressure at the permeate compartment.

The expressions “transchannel pressure differential” and “transchannelpressure (TCP)” are herein used synonymously to describe the pressuredifferential between an inlet of a flow channel to an outlet of the flowchannel, and is given by:

TCP=P _(inlet) −P _(R);  (4)

where P_(inlet)=pressure at the inlet of the flow channel; and

P_(R)=pressure at the outlet of the flow channel.

The term “dimensionless length” is used herein to describe a product ofchannel length, L, and the specific membrane area, σ_(c) from equation1, of a channel, and is defined by the following equation:

λ=σ_(c) L.  (5)

The dimensionless length of a stage in a multi-stage system is given bythe sum of the dimensionless lengths of the channels in the longestserial path in the stage as follows:

$\begin{matrix}{{\lambda_{stage} = {\sum\limits_{j = 1}^{m}{\sigma_{c,j}L_{j}}}};} & (6)\end{matrix}$

where m is the number of channels in the longest serial path in thestageσ_(c,j) is the σ_(c) of channel j in the longest serial path; and

L_(j) is the length of the j^(th) channel.

The dimensionless length of a system in a multi-stage system having nstages is given by the sum of the dimensionless length of the stages ofthe system as follows:

$\begin{matrix}{\lambda_{system} = {\sum\limits_{i = 1}^{n}\lambda_{{stage},{i;}}}} & (7)\end{matrix}$

where n is the number of stages in the system; andλ_(stage,i) is the λ for the i^(th) stage.

The term “ultrafiltration membranes” and “UF membranes” are used hereinto refer to membranes that have pore sizes in the range between about 1nanometer to about 100 nanometers. The term “microfiltration membranes”and “MF membranes” are used herein to refer to membranes that have poresizes in the range between about 0.1 micrometers to about 10micrometers. UF membranes are useful, for example, for the separation ofpolymeric molecules from water and other low molecular weight solutes.Molecules that are too large to penetrate these pores are retained whilewater, dissolved salts and small molecules can pass through these pores.The retention behavior of a membrane forms the basis for characterizingUF membranes, known as the “molecular weight cut off” of the membranes,expressed in units of Daltons, and abbreviated as MWCO. In variousembodiments, the present invention utilizes ultrafiltration membraneshaving MWCO ratings in the range from about 1,000 Daltons to severalmillion Daltons.

It is understood, that an SPF or conventional TFF filtering process isstarted at a specific feed rate equal to zero and operated for a periodof time at specific feed flow rates at which SPF is practiced beforesettling at an operational specific feed rate. The conventional TFFprocesses operate at specific feed flow rates higher than SPF processes(e.g., rates time-averaged over a time interval of several minutes). Itis also understood that there may be minor pressure variations thatwould cause an SPF process to operate at an instantaneous or short termspecific feed flow rate higher than the desired specific feed flow rate.The term “continuously supplying the feed stream,” as used herein, isunderstood to mean supplying the feed stream at an average specific feedflow rate, for example averaged over one minute to several minutes.

Now referring to FIG. 2, a P&I diagram depicts an exemplary system 200operating as an SPF process according to the invention. The system 200includes an SPF membrane separation module 201 including a channel 202which in one embodiment has specific membrane area greater than about 40cm⁻¹. The channel 202 is fluidly coupled to a feed port 209 and aretentate port 212. The separation module 201 further includes apermeate compartment 203 fluidly coupled to a permeate outlet port 210.In one embodiment the permeate compartment 203 is at least partiallyformed by a filtration membrane and is disposed adjacent the channel202, and except for the permeate outlet port 210 is otherwise sealed.The system 200 further includes a pressure device 206 feeding a feedstream 207 into the module 201, a feed pressure sensor 208 and aretentate pressure sensor 213 to monitor the feed pressure and retentatepressure, respectively. The system 200 includes a backpressure valve 215(also referred to as retentate valve 215) is fluidly coupled toretentate port 212 and is located downstream from the retentate port212. In an alternative embodiment a permeate distributor (as describedbelow in conjunction with FIG. 21) can be used to further control theSPF process. In another embodiment, system 200 includes an optionaldiafiltrate stream supplied through optional diafiltration port 226enabling an SPF diafiltration process (as described below in conjunctionwith FIGS. 13A, 16A, 18A, 19A and 20).

In operation, the pressure device 206, in one embodiment a feed pump,controls the process in conjunction with the back pressure valve 215. Incontrast to conventional separation modules which operate at specificfeed flow rates typically greater than 300 lmh, the pressure device 206feeds fluid at a rate such that the SPF process operates at specificfeed flow rates of less than about 200 lmh and in other embodiments atspecific feed flow rates of less that about 100 lmh. In one embodiment,the feed stream is continuously supplied at an inlet pressure greaterthan about 60 psi whereas conventional TTF processes are generallyoperated at much lower inlet pressures. It is understood, that uponstartup a conventional system temporarily operates at a low specificfeed flow rate beginning at about zero. The pressure device 206continuously supplies the feed at low specific feed flow rates. Thechannel 202 is pressurized, for example, by the combined action ofpressure device 206 and the backpressure valve 215. Pressure sensors 208and 213 monitor the feed and retentate pressures, respectively. Invarious embodiments, the permeate compartment 203 is at or close toatmospheric pressure, and the permeate stream 211 is directed throughthe permeate port 210 for further downstream processing or storage, andin other embodiments, the pressure in the permeate compartment 203 maybe elevated by means of suitable hydraulic resistors coupled to thepermeate stream (not shown). The retentate stream 214 is directedthrough the retentate port 212 for further downstream processing orstorage.

In certain embodiments, high conversion in a single pass is obtained byemploying low specific feed rates. In general, when operating separationmodules and systems in an SPF mode, the conversion is determined byselecting any two of the following parameters: the feed flow rate, theretentate flow rate, the permeate flow rate, specific feed rate, TMP andTCP. Selecting and controlling two of these parameters determines thevalues of the remaining parameters. In these embodiments, one directmethod for controlling the process is to measure the conversion andadjust either the feed or retentate flow rates in an iterative manner.Referring again to FIG. 2, in one embodiment the following steps areused with a feed pump as the pressure device 206 and the retentate valve215 to control the SPF process:

-   1. the permeation process is started by setting the flow rate of the    pressure device 206 to obtain a suitably low specific feed rate, F;-   2. retentate valve 215 is throttled until the desired TMP is    obtained;-   3. the conversion f is measured (by comparing flow rates or    concentrations by means of suitable sensors) after the process is    allowed to equilibrate;-   4. if the conversion is not close enough to the desired value, then    the flow rate through the pressure device 206 and the retentate    valve 215 are adjusted, up or down as follows:    -   a. if the conversion f is too high, the retentate valve 215 is        opened slightly, then the flow rate of pressure device 206 is        gradually increased until the feed pressure returns to its        initial value; these two adjustments lead to a small increase of        TCP and in turn a small increase of specific feed rate, F;    -   b. if the conversion f is too low, the flow rate of the pressure        device 206 is decreased by a small amount, then the retentate        valve 215 is closed slightly until the feed pressure returns to        its initial value; these two adjustments lead to a small        decrease of TCP and in turn a small decrease of specific feed        rate F; and-   5. steps 3 and 4 are repeated until the desired conversion f is    obtained.    Additionally, an SPF process can be operated by setting the    conversion to a predetermined factor by controlling the ratio of the    feed stream flow rate to the retentate stream flow rate. In one    embodiment, the ratio of the feed stream flow rate to the retentate    stream flow rate is provided by coupling the pumps in the feed and    retentate streams. In various embodiments, a specific feed rate    lower than about 200 lmh is used to obtain conversions exceeding    about 50%, and in other embodiments a specific feed rate lower than    about 100 lmh is used.

The pressure device 206 provides the driving forces to induce pressuredifferentials to affect the separation. SPF separations generallyinclude two distinct pressure differentials: a first pressuredifferential to drive liquid flow tangentially along the surface of themembrane, the TCP, and a second pressure differential to drive thepermeation across the membrane, the TMP. Pressure devices 206 forinducing the necessary pressure differentials include, but are notlimited to, compressed gases, vacuum sources, pumps and combinationsthereof. For example, a compressed gas can be used to drive the feedsolution, the same compressed gas at a lower pressure connected to theretentate receptacle can be used to control the TCP, while the permeateis kept at atmospheric pressure. This combination of two pressuresources can be used to provide the desired TCP and TMP. Alternatively, avacuum source may be used to drive the SPF separation process byconnecting a vacuum source, controlled at different vacuum levels, tothe permeate and retentate receptacles while the feed is kept atatmospheric pressure. This combination of two vacuum sources can also beused to provide the desired TCP and TMP. In some cases it may beconvenient to use both pressure and vacuum sources. There are a widevariety of vacuum and pressure sources well known to those skilled inthe art. For example, a vacuum source can be a liquid driven aspiratoror venturi, a central vacuum supply of the type commonly found inlaboratories, a dedicated vacuum pump, or combinations thereof. Adetailed list of means and devices for generating vacuums is given inPerry's Chemical Engineering Handbook, 6^(th) edition, McGraw-Hill,1984, at pp. 6-32 to 6-37. Suitable pressure sources include, forexample, compressed gases from a cylinder with conventional means forregulating the applied pressure, using pressurized gas from a centralsource commonly available in laboratories, using a dedicated compressorfrom among the types described, for example, in Section 6 of Perry'sChemical Engineering Handbook. Another suitable pressure device is aliquid pump. A wide variety of pumps are suitable for providing drivingforces in the methods and devices of the present invention. Examplesinclude peristaltic, syringe, centrifugal, piston, rotary lobe, and gearpumps. A detailed list of pumps is given in Perry's Chemical EngineeringHandbook, 6^(th) edition, McGraw-Hill, 1984, at pp. 6-4 to 6-17.

The separation module 201 comprises a filtration membrane including, butlimited to, one of a tubular, sheet and monolithic structure. Theseparation module 201 can use filtration membranes fabricated into anyof several topologies. Hollow fiber membranes are generally a tubularmembrane, with an inner diameter of typically between about 0.1 and 2.0millimeters whose inner or outer surface is the separating membrane. Invarious applications, the feed stream to be processed flows through theinside of the hollow fiber membrane, also referred to as the “lumen,”and the permeate leaves on the outside of the fibers. Sheet membranescan be made in various forms and typically are laminated to some sort ofcloth support. Two sheets of membrane separated by a highly permeablenet-like structure, or spacer, form the flow channel. A wide variety ofsheet membranes can be used in various embodiments of the presentinvention, including, but not limited to, non-planar sheets andmonolithic membranes. For example, membranes with undulating, dimpled orcorrugated surfaces are examples of non-planar sheet membranes. It ispossible to implement the SPF process using various separation modulesand housings including, but not limited to, a hollow fiber cartridge, aplate-and-frame assembly, a cassette and a spiral wound module.

In certain embodiments of the present invention, system 200 is used toconcentrate a retained species. In one embodiment, the concentrationprocess removes solvent from the feed stream as well as any other solutethat permeates through the membrane in a single pass. The result is theconcentration of those solutes that are retained by the membranes.Additionally, this concentration process purifies the retained speciesby the substantial removal of those species that permeate through themembrane. In other embodiments of the present invention, system 200 isused to perform a diafiltration processes in a single pass. In thesediafiltration embodiments, the solution that permeates through themembrane is replaced with another solution (also referred to as adiafiltrate or buffer) in order to change the composition of thesolution in which the retained solutes are dissolved. The addition ofthe diafiltrate can be performed, for example, substantiallysimultaneously with concentration, or sequentially in a series ofalternating concentration and diafiltration steps, or by a combinationof the two processes.

The specific membrane area of the channel 202, σ_(c), is in someembodiments greater than about 40 cm⁻¹, in other embodiments greaterthan about 50 cm⁻¹, and in other embodiments greater than about 100cm⁻¹. The specific feed rate, F, is in other embodiments less than about200 lmh, and in other embodiments less than about 100 lmh. Thedimensionless length, λ, is in some embodiments greater than about2,000, in other embodiments greater than about 3,000, and in yet otherembodiments greater than about 4,000. The operation of system 200 in SPFmode and continuously supplying the feed at a specific feed flow rate ofless than about 200 lmh overcomes or eliminates one or more of thedrawbacks associated with conventional TFF requiring recirculatingstreams. As compared to a conventional TFF separation modules andprocesses, the SPF process is enabled by low feed rates and long andthin channels as listed in Table 1, resulting in higher conversion in asingle-pass. As described below in conjunction with FIG. 7, the processof FIG. 2 can also be used in a multi-stage system provided either in aninternally or externally staged configuration to provide similaradvantages. SPF systems whether staged (internally or externally) orunstaged, and regardless of the means used to drive the filtrationprocess in various embodiments have one or more of the followingadvantages over conventional TFF systems:

-   1. high conversion in a single-pass, obtaining conversions greater    than about 50%, in other embodiments conversions greater than about    75%, and in yet other embodiments conversions greater than about    90%;-   2. simple, easier to control processes with lower hold-up volume;    and-   3. average residence times greater than about 2 seconds in some    cassette embodiments and greater than about 20 seconds for certain    hollow fiber embodiments, where the average residence time is equal    to the void volume of the flow channels divided by the average flow    rate in the channel (the approximate average of the feed flow rate    into the module and retentate flow rate out of the module).

TABLE 1 Conventional TFF Operation vs. SPF Operation TFF SPF SpecificFeed Rate F 300~1,500 lmh <200 lmh Specific Membrane Area <75 cm⁻¹ >40cm⁻¹ Process Batch process requiring Single-pass process recirculationloops Conversion Per Pass f <15% >50%It is understood that a process using SPF devices and operatingparameters could be operated in a batch mode. In these embodiments, theretentate stream from an SPF module is recirculated back to the feed.Such a process provides the advantage of smaller circulation rates andtherefore requires smaller hydraulic components, pumps and piping.

Referring to FIG. 3, a process and instrument diagram of a SPF processand system 300 similar to system 200 of FIG. 2, includes a SPF membraneseparation module 301 having pressurized tanks, feed tank 322 andretentate tank 323 in place of the pressure device 206 and the retentatevalve 215 of FIG. 2, respectively. The system 300 further includespressure regulators 325 and 326, connected to a compressed gas source327. It is noted that the SPF system embodiment of FIG. 3 does notinclude any pumps.

In operation, the two tanks 322, 323 are maintained at the desired feedand retentate pressures by means of the pressure regulators 325 and 326.The following steps are used with the pressurized feed tank 322 andretentate tank 323 to operate the filtration process:

-   1. the permeation process is started by setting the feed pressure    and the retentate pressure to initial values with pressure    regulators 325 and 326, respectively, thereby obtaining an initial    TCP, and a suitably low specific feed rate, F;-   2. the conversion f is measured after the process is allowed to    equilibrate;-   3. if the conversion is not close enough to the desired value, then    TCP is adjusted up or down by adjusting pressure regulator 326 as    follows:    -   a. if the conversion f is too high, reduce retentate pressure        313 slightly, which leads to a small increase of TCP and in turn        a small increase of specific feed rate, F;    -   b. if the conversion f is too low, increase retentate pressure        313 slightly, which leads to a small decrease of TCP and in turn        a small decrease of specific feed rate, F;-   4. steps 2 and 3 are repeated until the desired conversion is    obtained.

Referring to FIG. 4A, a process and instrument diagram of another SPFprocess and system 400 similar to system 200 of FIG. 2, includes an SPFmembrane separation module 401 and a feed pump 406 and a retentate pump429 instead of backpressure valve 215 to drive and control the process.The feed pump 406 is set to obtain a suitably low specific feed rate, F,while the retentate pump 429 can be set at the flow rate necessary toobtain the desired conversion, f. The feed pressure 408 of a feed stream407 and retentate pressure 413 of a retentate stream 414 are notdirectly set but instead result from the previously set feed andretentate flow rates. If the feed pressure 408 exceeds the maximumallowed by the equipment, then the flow rates of pumps 406 and 429 areproportionately reduced in steps until the feed pressure 408 is at orbelow the maximum allowable pressure. Referring to FIG. 4B, a processand system 400′ represented in FIG. 4B similar to system 400, includesan SPF membrane separation module 401 and a feed pump 406 and permeatepump 430 instead of retentate pump 429 to drive and control the process.The feed pump 406 can be set to obtain a suitably low specific feedrate, F, while the permeate pump 430 can be set at the flow ratenecessary to obtain the desired conversion, f. The feed pressure 408 andthe permeate pressure 431 are not directly set, but instead result fromthe feed and permeate flow rates previously set. If the feed pressure408 exceeds the maximum allowed by the equipment, then the flow rates ofpumps 406 and 430 is proportionately reduced in small steps until thefeed pressure 408 is at or below the maximum allowable. In this case thepermeate pressure 431 may be below atmospheric depending on the pressureof retentate stream 414 (if the retentate stream 414 is at or nearatmospheric pressure, then the permeate 411 will be below atmospheric;if the permeate pressure 431 is close to a full vacuum, then the flowrates of both pumps 406 and 430 are reduced to achieve the desiredconversion. In an alternative embodiment, system 400′ optionallyincludes a flow ratio controller 434 interposed between the feed pump406 and the permeate pump 430 and fluidly coupled to the feed stream 407and retentate stream 414. The flow ratio controller 434 enables settingthe conversion to a predetermined factor.

In the various embodiments of the SPF system and process according tothe invention, as described in conjunction with the process andinstrument diagrams of FIGS. 2, 3, 4A and 4B, the process can bepartially controlled by controlling the transchannel pressuredifferential, TCP. In various embodiments of a TCP-control approach, forexample using system 400′, the feed pressure 408 is maintained at atargeted value, typically near the highest pressure allowed by theequipment, and by adjusting the feed rate and the retentate pressure tochange the TCP until the desired conversion, f, is obtained. Generally,a higher TCP results in a lower conversion. In other embodiments, theprocess can be controlled by controlling the TMP. Such embodiments areuseful, for example, whenever the flux is sensitive to changes in TMP.In various embodiments of a TMP-control approach, the TCP is maintainedat a targeted value by maintaining a constant feed flow rate whileadjusting the retentate pressure until the desired conversion, f, isobtained. Generally a higher TMP results in a higher conversion.

In various embodiments, the SPF systems and processes of the presentinvention, employing specific feed rates of less than about 200 lmh, andin other embodiments less than about 100 lmh, to obtain conversionsgreater than about 50%, have several practical advantages, as follows:

-   1. the single pass process is a substantially continuous processes,    where the feed stream is exposed to the processing equipment for a    decreased amount of time;-   2. the single pass process has operating conditions that do not    require continual adjustment since the feed stream does not change    (e.g., in viscosity) unlike in a batch process; and-   3. the single pass process has flow rates of feed stream and    retentate stream that are typically 3-20 times smaller than those    necessary on an equivalently-sized conventional TFF process    utilizing recirculation loops, resulting in lower hold-up volume due    to the smaller diameter of the pipes; and-   4. the single pass process does not require a feed tank since the    feed stream coming from an upstream process could be fed directly    into the SPF module. The elimination of the tank reduces the    equipment cost, the floor space occupied by the equipment, and the    hold-up volume.

Now referring to FIG. 5, an exemplary hollow fiber module 500 includes ahousing 502 and a hollow fiber ultrafiltration membrane 542 disposedwithin the housing 502. The membrane 542 forms a flow channel 541. Themodule 500 further includes seals 543 disposed adjacent a channel inlet544 and a channel outlet 545 to separate the feed stream in the channel541 from the permeate compartment 546. In operation, the feed streamenters the flow channel 541 at the channel inlet 544, flowingtangentially over the membrane 542 towards the channel outlet 545,driven by, for example, a transchannel pressure differential, TCP, and atransmembrane pressure differential, TMP, generated by at least onepressure source (not shown). As a result of the TMP a portion of thefeed permeates through the membrane 542, as indicated by flow arrowsfrom the channel 541 into the permeate compartment 546, providing thepermeate in the permeate compartment 546. The flow channel 541 formed bythe hollow fiber membrane 542 is further described by its length, L, andlumen diameter, d, as shown in FIG. 5. Flow channels formed with hollowfiber membranes are typically open with no flow obstructions. Thespecific membrane area, a, of the flow channel 541 is defined as theratio of the membrane area contained in the channels divided by the voidvolume of the channel 541. For channels formed with hollow fibermembranes the specific membrane area is derived from equation 1 as:

$\begin{matrix}{\sigma_{C} = {\frac{4}{d}.}} & (8)\end{matrix}$

Where d is the diameter of the lumen.

In one embodiment, the flow channel 541 has a specific membrane areagreater than about 50 cm⁻¹, and in this embodiment the membrane has ahydraulic permeability greater than about 2 lmh/psi. In anotherembodiment the specific membrane area is greater than about 80 cm⁻¹, andin yet another embodiment the specific membrane area is at least about130 cm⁻¹. High specific membrane areas result in higher flux and reducedhold-up-volume of the TFF module. For hollow fiber channels thedimensionless length is given by:

$\begin{matrix}{\lambda = {4{\frac{L}{d}.}}} & (9)\end{matrix}$

Where d is the diameter of the lumen; and L is the length of the lumen.

In one embodiment the dimensionless length, λ, of the flow channel of amodule comprising hollow fiber flow channels is greater than about2,000, in another embodiment greater than about 4,000 and in yet anotherembodiment greater than 10,000. The values of specific membrane area,σ_(c), and dimensionless length, λ, in these embodiments enable thehollow fiber module 500 to function effectively in a SPF process similarto the process described in FIG. 2.

Referring to FIG. 6, an exemplary flat sheet module 600 includes ahousing 602, an SPF channel 641, disposed within the housing 602,including a flat-sheet membrane 642 disposed adjacent a spacer 655 andseals 643 disposed adjacent a channel inlet 644 and a channel outlet 645providing the channel 641 on one side of the membrane 642 and a permeatecompartment 646 on the other side of the membrane 642. In oneembodiment, channel 641 is formed by sandwiching the spacer 655 betweentwo sheets of flat-sheet membrane 642. Channel 641 formed in this manneris referred to as a rectangular channel since it possesses a rectangularcross-section, although it is to be understood that SPF channels are notlimited to rectangular cross-sections or any specific topology.

In operation the feed stream enters the channel inlet 644 of the channel641 and flows tangentially over the membrane surface 642 towards channeloutlet 645 of the channel 641, driven, for example, a transchannelpressure differential, TCP, and a transmembrane pressure differential,TMP, generated by at least one pressure source (not shown). As a resultof the TMP a portion of the feed permeates through the membrane 642 asshown by flow arrows from the channel 641 thereby providing thepermeate. The channel 641, here formed by the flat-sheet membrane 642can be partially described by its length, L, width (not shown) andheight, h. The feed stream can be distributed across the width of thechannel 641 by appropriate feed distributors (not shown). The retentatecan be collected along the width of the channel 641 by appropriateretentate distributors (not shown). The spacer 655 maintains themembranes in a spaced apart arrangement, and edge seals 643 enclose thechannel 641 and form a portion of the permeate compartment 646. Thereare numerous techniques for forming edge seals known to those skilled inthe art. The spacer 655 can be a woven, non-woven, or molded structure,or combinations thereof, that allow the percolation of liquid betweenits solid structures but are also sufficiently rigid to maintain thechannel height h when exposed to compressive loads. The “void fraction”of the spacer 655, E, defined as the ratio of the void volume containedwithin the spacer to the total volume occupied by the spacer 655, is anparameter known to one skilled in the art, and the structure of thespacer 655 affects the void volume as well as the hydraulic resistanceof the channel 641. In one embodiment the spacer 655 is aturbulence-promoting spacer.

The calculation of the specific membrane area σ_(c), the dimensionlesslength λ, and the specific feed flow rate F can be provided for aspecific channel geometry using the channel height h, and void fraction,ε. For example, for rectangular channels, the specific membrane area ofthe channel is derived from equation 1 as follows:

$\begin{matrix}{\sigma_{C} = {\frac{2}{ɛ\; h}.}} & (10)\end{matrix}$

Where h is the height of the channel; and

ε is the void fraction of the spacer.The dimensionless length λ is derived from equation 5 as follows:

$\begin{matrix}{\lambda = {2{\frac{L}{ɛ\; h}.}}} & (11)\end{matrix}$

Where L is the length of the channel

h is the height of the channel; andε is the void fraction of the spacer.Specific formulas for these parameters for channels having alternativetopologies can be derived from the dimensions of the channel 641 or cancomputed empirically as is known in the art. In one embodiment, thechannel 641 has a specific membrane area greater than about 40 cm⁻¹ andin another embodiment the channel 641 has a specific membrane areagreater than about 50 cm⁻¹. The specific values of specific membranearea, σ_(c), and dimensionless length, λ, in these embodiments enablethe channel 641 to function effectively in a single-pass process runcontinuously at low specific feed flow rates, F, similar to the processdescribed in FIG. 2.

Now referring to FIG. 7A, an SPF system 700 for the filtration ofliquids using an SPF process, includes a plurality of stages 702 and704, each stage having a plurality of channels 712 a-712 g and 712 h-712m (collectively referred to as channels 712), respectively. The system700 further includes a pressure device 708 fluidly coupled to the firststage. The system 700 can optionally include a stage 706 with a singlechannel 712 m. The stages 702 and 704 are disposed such that each stageis in fluid communication with each adjacent stage preceding it and isin fluid communication with each adjacent stage that follows it (i.e.,the retentate from the i^(th) stage becomes the feed of the (i+1)^(th)stage). Each of the channels 712 comprises a filtration membrane. Asdescribed above, each of the channels 712 has a length, a membrane area,a void volume, a specific membrane area expressed as a ratio of themembrane area to the void volume, and a dimensionless length expressedas a product of the channel length and the specific membrane area. Inthe configuration of FIG. 7A, the dimensionless length of each stage702, 704 and 706 is equal to the dimensionless length of the longest ofchannel 712 in each stage. It is understood that the channels 712 couldbe identical or could have varying properties, a stage could havemultiple channels in series, in parallel, in a series parallelarrangement, and that the number of stages in system 700 could begreater than three.

In one embodiment the channels 712 in any one of the stages 702 and 704are substantially identical. In the embodiment of FIG. 7A the firststage 702 has a greater number of channels than the second stage 704although in other embodiments the stages 702 and 704 could have the samenumber of channels. The system 700 can be implemented as eitherinternally or externally staged system. In an internally staged system ahousing, for example a cassette holder having two flat plates, includesthe stages 702, 704 and 706 and is generally sealed and has externalfeed, permeate and retentate connections. In an externally staged systemthe stages are coupled together with discrete external connections. Herethe flow paths through channels 712 are connected by serially connectingstages 702, 704, and 706 together, thereby forming a serial flow path inthe feed/retentate compartments, instead of the conventional parallelconnections in TFF systems. Thus the resulting effective channel (i.e.,the serial combination of channels) in an SPF embodiment ischaracterized as being a relatively long thin channel as compared tochannels in conventional systems.

System 700 is operated in SPF mode as described above in conjunctionwith FIG. 2, (i.e. continuously supplying the feed stream at arelatively low specific feed flow rate using a relatively small feedsupply device). Separation performance is maintained in the stages 702,704, and 706 by varying at least one filtration property of one stagerelative to a preceding stage so as to match the separation propertiesof the stage to the conditions of the feed stream at that stage. Afiltration property is a stage property which affects, for example, theconversion, the TMP, and flux performance, and includes but is notlimited to the cross-sectional flow area of the stage, the specificmembrane area of the stage, the number of channels in the stage, thehydraulic diameter of a feed spacer disposed adjacent the membrane andwithin the channel of a stage, the dimensionless length, and thefiltration membrane properties. Here the variation in stage propertiesof stages 702, 704, and 706, is the number of channels 712 per stage.One result of changing the number of channels 712 per stage is to affectthe velocity of the feed stream so that flux performance is maintainedunder conditions of high conversion throughout the stages 702, 704 and706. It is noted that varying the number of channels 712 per stage issimilar to varying the cross sectional area of the stages.

A further advantage to staging in an SPF system is that staging allows along flow path without excessive pressure drops. Another advantage ofthe present invention is the elimination of the need to include a pumpor other pressure source between stages. Also, a biopharmaceutical feedstream can be efficiently processed using conventional filtrationmembranes with well understood properties in system 700 while achievinga relatively high conversion and reducing system complexity, hold-upvolume and exposure time. There are numerous ways of arranging channelsand stages in both internally-staged module and externally-stagedsystems, including, but not limited to, modules comprising differenttypes of filtration membranes, for example, (a) hollow fiber membranes,(b) flat-sheet membranes, and (c) membrane monoliths. Staging in whichthe cross-sectional area for flow of the module decreases along the flowpath, can be provided in several ways. In other embodiments, suitablefor almost all membranes, one approach is to decrease the number ofchannels in each stage along the flow path, the dimensions of eachchannel being substantially the same in all stages. In otherembodiments, where the stages comprise rectangular channels, one methodis to reduce the width of the channel along the flow path while keepingthe specific membrane area of the channel substantially the same. Instill other embodiments, the channel width varies continuously along theflow path, with the width at an inlet of the channel of a stage beinggreater than the width at an outlet of the channel, and in one examplethe inlet width is about 1.2 times greater than the outlet width. Inother embodiments the inlet width of the channel is about two timesgreater than the outlet width. In some other embodiments, channelshaving a continuously varying width are used in conjunction with astaged system, and in still other embodiments, un-staged modules includechannels having a continuously varying width. These methods for reducingthe cross-sectional area can be combined.

The staging in system 700 is generally referred to as retentate stagingbecause the retentate from one stage serves as a feed to the next stage.The boundary between a stage and an adjacent following stage in an SPFmulti-stage system can be provided in a number of additional ways. Atransition in a physical property of the membrane in the channels candefine a stage boundary. For example the membrane filter, thedimensionless length of the channels, the hydraulic diameter of thespacer in the channel, the thickness of the flow channels and the totalcross-section for feed flow may change between stages. A stagetransition also occurs where there is a discontinuity in the compositionof the fluid between a stage and an adjacent stage. This type ofdiscontinuity is affected, for example, by introducing a diafiltrationstream at the boundary of two stages. In a diafiltration system, thestage can include the same number of substantially identical channels asthe adjacent preceding stage, and SPF operation is enabled by theintroduction of diafiltrate at the intersection of two stages asdescribed below in conjunction with FIGS. 13A, 13B, 18A, 18B, 19A, 19Band 20. Another form of stage transition can be provided by adiscontinuity in the operating conditions of the separation process, forexample, transmembrane pressure in the adjacent stages. Such atransition can be achieved, for example, by a discontinuous change inthe pressure of the permeate compartment, the feed compartment, or both.In alternative embodiments the property change can include providingpermeate control in each stage as discussed below in conjunction withFIG. 21. A stage transition can also be provided by applying externalcontrols. For example, providing heating or cooling at various stages insystem 700. The tailoring of physical properties or operating conditionsto each stage leads to improved separation processes. In certainmulti-stage embodiments, SPF operation can be achieved without therequirement of σ_(c), being greater than about 40 cm⁻¹.

In various embodiments, SPF modules with internal staging comprise oneor more of: (a) decreased cross-sectional area for flow along the flowpath so as to boost the liquid velocity within the flow channel tocompensate for the lower velocity induced by permeation and therebyboost the flux performance of the flow channel; (b) increased specificmembrane area of the channel along the flow path so as to boost the fluxperformance of the channel; (c) changed permeation properties of themembrane along the flow path so as to optimize the balance between fluxand rejection in any given stage; and (d) ports and flow passages forthe introduction of the diafiltrate at various points along the flowpath. Internally-staged modules having some of the properties describedabove are described below in conjunction with FIGS. 8B, 8C, 9A, and 9B.

In one embodiment using flat-sheet membranes, the cross-sectional areaof a channel is reduced by decreasing the width of the channel along theflow path. The channel height can be varied within the channel, but thisalternative is less practical. It has been recognized that theseproperty changes increase efficiency because high conversion leads tolower liquid velocities within a channel. The lower velocities have twopotential consequences: reduced flux due to a diminished sweepingaction, and reduced TCP. While the lower flux is generally anunfavorable consequence of high conversion, the lower pressure drop perunit of flow path length enables an increase in the overall flow pathlength which leads to higher single pass concentration factors withoutresulting in excessive inlet pressures. Property changes along the flowpath are implemented so as to increase the flux of the module, forexample, by taking advantage of the reduced TCP obtained by using theSPF process. Changing the sieving coefficient also leads to improvedseparation effectiveness. In certain embodiments, the channels in themodule have a substantially continuously changing physical propertyalong the flow path or can change discretely as in FIG. 7A. In otherembodiments the property change is monotonic between each stage and anadjacent following stage. SPF modules and systems using membranemonoliths (e.g., ceramic membranes) are similar in structure and operatesimilarly to hollow fibers modules and systems as described below.

Further detailed descriptions of various embodiments ofinternally-staged modules with staging are discussed in the context ofFIGS. 7B, 7C, 8B and 8C. FIGS. 7B and 7C are schematic diagrams ofvarious embodiments of the cross-section of internally-staged modules inwhich the staging property change is accomplished by reducing thecross-sectional area for flow along the flow path while maintainingsubstantially the same channel dimensions, and therefore, maintainingsubstantially the same specific membrane area of the channel.

Referring to FIG. 7B, an exemplary module 718 comprises a housing 720,stages 722 a, 722 b-722 n (collectively referred to as stages 722)having a plurality of substantially identical channels 724, hererectangular channels disposed within the housing 720. Each channel 724comprises a membrane 726 disposed adjacent to a feed spacer 728 whichprovides support for the membrane 726. In one embodiment, the channels724 have σ_(c) values of greater than about 40 cm⁻¹ and λ values of lessthan about 6,000. In this embodiment, λ_(stage) is equal to λ becausethere is one channel 724 in the longest serial flow path in the stage,and the λ_(system) (i.e., the λ of the module) for module 718 is the sumof the dimensionless lengths of the stages 722 and is in one embodimentgreater than 2,000. The module 718 further includes an inlet manifold730 and outlet manifold 732 fluidly coupled to the channels 724 of thefirst stage 722 a, an inlet manifold 736 and outlet manifold 738 fluidlycoupled to the channels 724 of the second stage 722 b, and a passageway734 fluidly coupling outlet manifold 732 with inlet manifold 736. It isunderstood that module 718 can comprise several additional stages 722having the same or different number of channels 724 coupled precedingand following stages 722 in a similar way as stages 722 a and 722 b suchthat each stage 722 is in fluid communication with each adjacent stage722 preceding it and is in fluid communication with each adjacent stage722 that follows it. The module 718 further includes an inlet manifold740 and outlet manifold 746 fluidly coupled to the channels 724 of thefinal stage 722 n. The outlet manifold 746 disposed in the housingprovides the retentate output for further processing through a retentateport (not shown). Module 718 also includes a feed and a permeate ports(not shown).

In the embodiment of FIG. 7B, the first stage 722 a comprises fourchannels, and is followed by and is fluidly coupled to the adjacentsecond stage 722 b which comprises two channels 724. Here the finalstage 722 n comprises a single channel 724. While the permeate from thethree stages 722 can be collected together in parallel (for claritypermeate connections are not shown), the retentate from one stage 722becomes the feed to the following adjacent stage 722; more specifically,the retentate of the first stage 722 a becomes the feed of the secondstage 722 b, and the retentate of the second stage 722 b becomes thefeed to the final stage 722 n. Since the channels 724 have substantiallythe same channel height, length and width in the stages 722, here forexample, the cross-sectional area of the final stage 722 n is half thatof the second stage 722 b, which in turn is half that of the first stage722 a. This results in adjacent stages having a cross-sectional arearatio equal to about 0.5.

In one embodiment, the channels 724 are straight. However, it is to beunderstood that the channels 724 need not be straight; but rather can bestraight, coiled, arranged in zigzag fashion, and in general can haveany topology wherein an effective tangential flow across the membrane726 can be maintained. Although three stages 722 are shown in FIGS. 7Band 7C, it is understood that the embodiments of internally-stagedmodules of the present invention are not limited to three stages; ratherother embodiments can include two-stages as well as those with more thanthree stages.

In various embodiments, the properties of the membrane 726 change ineach stage 722 along the flow path. It is known to those skilled in theart that a small change in the retention of an ultrafiltration membrane(e.g., from 99% to 99.9%) often results in a significant change in thehydraulic permeability of the membrane. The membrane with the higherretention is referred to as a “tight” membrane, while the membrane withthe lower retention is referred to as a “loose” membrane. Thisphenomenon is exploited in various embodiments by increasing theretention of the membrane 726 along the flow path. In variousembodiments, the higher flux characteristic of looser membranes in theupstream stages can be used advantageously, while decreasing, orpreventing, excessive permeation losses by using tighter membranes inthe downstream stages. Different applications can take advantage ofchanging different membrane properties in this kind of staging.

In addition to the channel properties variations described above,channel properties can be changed by: changing the specific membranearea; changing the filtration membrane properties; changing thehydraulic diameter of the feed spacer 728. The hydraulic diameter isrelated to flow resistance and is a function of the spacer properties. Achange in the membrane property includes a change in membranepermeability and a change in the MWCO of the membrane. In one embodimentthe ratio of the cross-sectional area of a first stage to thecross-sectional area of a second stage is greater than about 1.1. Inanother embodiment, the ratio of the specific membrane area of a channelin the first stage to the specific membrane area of a channel in thesecond stage is greater than about 1.25. In still another embodiment,the ratio of the cross-sectional area of the first stage to thecross-sectional area of the second stage is less than about 0.8. Themodule 718 is operated in SPF mode as described above in conjunctionwith FIGS. 2 and 7A.

Certain higher flux applications are realized using embodimentscomprising high permeability ultrafiltration membranes, with σ_(c)values of greater than 40 cm⁻¹. In such embodiments, it is beneficial tolimit the value of λ_(stage) in order to limit the change in fluidvelocity or concentration in a stage and thus to make the transition tothe next stage, where the next stage has properties more suited to thereduced fluid velocity or higher concentration. If the viscosity of theflowing material rises significantly, it may be desirable to increasethe hydraulic diameter of the channels in the stages at frequentintervals in order to limit the pressure drop. If the concentration ofthe species that is being retained becomes very high, it is beneficialto use tighter membranes or membranes with lower molecular weightcut-offs in the downstream stages in order to reduce losses of theretained species in the permeate. However, when using stages withlimited values of λ_(stage) the value of λ_(system) must nevertheless belarge enough to achieve the total concentration factor or conversiondesired.

When diafiltration is used, limiting the value of λ_(stage) results inthe use of a larger number of stages for a given degree of impurityremoval and results in a lower consumption of diafiltrate. In someembodiments, it is particularly beneficial to limit the value ofλ_(stage) to less than 3,500, while increasing the value of λ_(system)to more than 2,000 in staged systems which use modules with a σ_(c)value of greater than 40 cm⁻¹. There is no particular limit on thelowest value of λ_(stage), aside from the expense of using a largenumber of small stages. In some embodiments, more that two stages areused and in other embodiments more than four stages are used. Theshorter stages (i.e. having smaller values of λ_(stage)) allow for finercontrol of the property changes among stages and this controlcontributes to maintaining the fluid velocity along the flow path at adesirable value. It should be understood that the higher the flux (thehigher the hydraulic permeability of the membrane) the shorter the stageneeds to be. Therefore, there is an inverse relation between hydraulicpermeability of the membrane and λ_(stage). In one embodiment, theinitial hydraulic permeability of the membrane (i.e., before themembrane is conditioned by use) is greater than about 0.5 lmh/psi. Inother embodiments, staging maintains the separation performance insingle pass operation by affecting at least one of: a transmembranepressure (TMP); a feed stream velocity; and a bulk concentration of thesolute. Each stage in these embodiments is designed to provide desirableconditions in each stage.

Referring to FIG. 7C, a module 760 comprises three stages 757, 758 and759 comprising hollow fiber channels 743. The first stage 757 isfollowed by the second stage 758 and finally the third stage 759, eachstage comprising, in this example, 104, 52, and 26 channels,respectively. The stages 757, 758 and 759 can be fluidly coupled usingtechniques known in the art and also in arrangements described inconjunction with FIGS. 16A-18B. In operation, the permeate from thethree stages is collected together, the retentate from one stage becomesthe feed to the adjacent following stage. The retentate of the firststage 757 becomes the feed of the second stage 758, and the retentate ofthe second stage 758 becomes the feed of third stage 759. Since thechannels 743 in this example have substantially the same lumen diameterand length in the three stages 757, 758 and 759, the cross-sectionalarea of the third stage 759 is half that of the second stage 758, whichin turn is half that of the first stage 757. This results in contiguousstages having a cross-sectional area ratio equal to about 0.5. Themodule 760 is operated in SPF mode as described above in conjunctionwith FIGS. 2 and 7A.

Now referring to FIG. 7D, a system for the ultrafiltration of liquids700′ similar to the system 700 of FIG. 7A includes a plurality ofsubstantially identical stages 772 a-772 n (collectively referred to asstages 772), each stage 772 having a plurality of channels 774. Here,each stage 772 has a series-parallel arrangement of channels in a “threeover two” configuration. As described above, each of the channels 774has a length, a membrane area, a void volume, a specific membrane areaσ_(c) expressed as a ratio of the membrane area to the void volume, anda dimensionless length λ expressed as a product of the channel lengthand the specific membrane area. In the configuration of FIG. 7D, thedimensionless length of each stage 772 is equal to the dimensionlesslength of the longest serial flow path 776 of each stage 772. In thisexample, the dimensionless length of each stage 772 λ_(stage) would be3*λ, and dimensionless length of the system 700′, λ_(system) would be9*λ. In one embodiment, the specific membrane area of channel 774 isgreater than about 40 cm⁻¹, dimensionless length of the system isgreater than about 2,000 and the dimensionless length of at least one ofthe plurality of stages is less than about 6,000. In an alternativeembodiment, the dimensionless length of the system is greater than about4,000 and the dimensionless length of the at least one of the pluralityof stages is less than about 3,500. By using relatively short flow paths(i.e., small values of λ_(stage)) for individual stages the fluidvelocity can be maintained at reasonable levels in any given stage. Byusing large values for the overall system flow path length (large valuesof λ_(system)) a high degree of concentration is achieved. Even thoughthe stages 772 have flow path with unequal length, system 700′ can beoperated in SPF mode as described above in conjunction with FIGS. 2 and7A although not as efficiently as a system with stages having equal flowpath lengths.

Now referring to FIG. 8A, an exemplary module for the ultrafiltration ofliquids 800 includes stages 804 and 814 in which the staging isaccomplished by increasing the specific membrane area of the stage alongthe flow path while maintaining substantially the same number ofchannels in each stage, here, one channel. Here channel 816 in stage 814is thinner than channel 806 in stage 804. Since the volumetric flow rateat the exit of 804 is the same as the volumetric flow rate at the inletof 814, the effect of the thinner channel length is to increase thevelocity in stage 814. It is understood that the specific membrane areaof the stage and the height of the channels are related and thatchanging a spacer property can change the specific membrane area of thestage. Furthermore, the specific membrane area of a stage can be changedwithout changing the cross section for flow of the stage.

Referring to FIG. 8B, a module 840 comprises three stages 847, 848 and849 made with rectangular channels 841. The first stage 847 is followedby the second stage 848 and finally the third stage 849, each stagehaving the same number of rectangular channels 841, 841′ and 841″,respectively. For clarity, the flow channels represented by FIGS. 8B and8C are depicted as straight and rectangular. However, it is to beunderstood that the flow channels need not be straight or rectangular;but rather can be coiled, arranged in zigzag fashion, and in general canhave any topology which supports tangential flow. Although three stagesare shown in FIGS. 8B and 8C, it is to be understood that theinternally-staged embodiments of the present invention are not limitedto three stages. The stages 847, 848 and 849 can be fluidly coupledusing techniques known in the art and similar to the arrangementdescribed in conjunction with FIG. 13B (without the diafiltrationdistributor).

In operation, the permeate from the three stages is collected togetherand the retentate from one stage becomes the feed to the contiguousstage downstream, more specifically, the retentate of the first stage847 becomes the feed of the second stage 848, and the retentate of thesecond stage 848 becomes the feed of the third stage 849. Here therectangular channels 841, 841′ and 841″ have different heights. Thespecific membrane area of each stage increases along the flow path byvirtue of a decreasing channel height, contiguous stages having aspecific membrane area ratio, equal to about two, with a correspondingchannel height ratio, equal to about 0.5. As a result, thecross-sectional area of the third stage 869 is half that of the secondstage 848, which in turn is half that of the first stage 847. In thisembodiment, the contiguous stages have a cross-sectional area ratio,equal to about 0.5. In various other embodiments it is possible to havea cross-sectional area ratio equal to 1.0 while still keeping thespecific membrane area ratio equal to about 2.0, for example, bydoubling the number of channels in each subsequent stage. Therefore, forembodiments in which the specific membrane area ratio increases it ispossible to have the cross-sectional area ratio decrease as representedby FIG. 8A, stay the same as described here, or even increase, bychanging the number of channels in each stage along the flow path.

Referring to FIG. 8C, a module 860 according to the invention comprisesthree stages 867, 868 and 869. Stage 867 comprises a plurality of hollowfiber channels 863, stage 868 comprises a plurality of hollow fiberchannels 863′ and stage 869 comprises a plurality of hollow fiberchannels 863″. The first stage 867 is followed by the second stage 868and finally the third stage 869, here, each stage has the same number ofhollow fiber channels, but the hollow fiber channels in each stage havedifferent diameters. The specific membrane area of each stage 867, 868and 869 increases along the flow path due to a decreasing lumendiameter. With a corresponding lumen diameter ratio, equal to about0.707 for example, adjacent stages have a specific membrane area ratioequal to about 1.41. As a result, the cross-sectional area of the thirdstage 869 is half that of the second stage 868, which in turn is halfthat of the first stage 867. Here, the adjacent stages have across-sectional area ratio equal to about 0.5. In other embodiments itis possible to have a cross-sectional area ratio equal to approximately1.0 while still keeping the specific membrane area ratio equal to about1.41, for example, by increasing the number of channels in eachsubsequent stage by about 41%. Therefore, for embodiments in which thespecific membrane area ratio increases it is possible to have thecross-sectional area ratio (a) decrease (as represented by FIG. 8B),stay the same or even increase, by changing the number of channels ineach stage along the flow path.

The permeates from the three stages are collected together and theretentate from one stage becomes the feed to the adjacent followingstage; more specifically, the retentate of the first stage 867 becomesthe feed of the second stage 868, and the retentate of the second stage868 becomes the feed of the third stage 869. The stages 867, 868 and 869can be fluidly coupled using techniques known in the art. In general,any number of stages greater than two can be used in theinternally-staged or externally staged embodiments of the presentinvention. In certain applications, the number of stages chosen is basedon a tradeoff between module cost and the benefits of improvedperformance offered by an increased number of stages, for example higherflux and finer TMP control. Some embodiments have fewer than twentystages, and other embodiments have fewer than ten stages. The ratio ofthe change in separation properties between stages is based on a numberof factors including the number of stages and the overall separationobjective desired for the system. In various embodiments of stagingbased on decreasing the cross-sectional area of stages, cross-sectionalarea ratios of about 0.3 to about 0.9 are used, with a ratio range ofabout 0.5 to about 0.8 in other embodiments. In various embodiments ofstaging based on increasing the specific membrane area of stages,specific membrane area ratios of about 1.2 to 3.0 are used, with aspecific membrane area ratio range of about 1.3 to about 2.0 in otherembodiments. In still other embodiments of staging based on increasingthe retention of the membrane on each stage, the ratio of the sievingcoefficient of the retained species, of about 0.1 to 0.75 are used, witha range of about 0.1 to about 0.50 in other embodiments.

High fluxes made possible by the use of modules, comprising filtrationmembranes channels, with σ_(c) values of greater than about 40 cm⁻¹. Itis beneficial to limit the value of λ_(stage) for these modules in orderto limit the change in fluid velocity or concentration in the stage andthus to make the transition to the next stage, where the next stage mayhave properties more suited to the reduced fluid velocity or higherconcentration. However the value of λ_(system) must be large enough toprovide the desired concentration. One embodiment limits the value ofλ_(stage) to less than about 6,000, with the value of λ_(system) beinggreater that about 4,000 in staged systems with channels having a σ_(c)value of greater than about 40 cm⁻¹. There is no particular limit on thelowest value of λ_(stage) aside from the complexity and expense of usinga large number of short stages. The limitation on λ_(stage) is alsoapplicable to modules including hollow fiber membranes.

Referring now to FIG. 9A, a non-staged module 900 according to theinvention has a substantially continuously changing physical propertyalong the flow path. Module 900 includes a feed compartment 970comprising a feed spacer 971 and a sealant forming shell 972. The module900 includes a plurality of secondary flow passages 976, fluidly coupledto a plurality of feed primary flow passages 975. The module 900 furtherincludes ribs 973 disposed adjacent the feed spacer 971 forming achannel 974 whose width diminishes along the channel length. In oneembodiment the ribs 973 are molded into the feed spacer 971. The module900 further includes secondary flow passage 977 fluidly coupled toretentate primary flow passage 978 and permeate primary passages 982coupled to a permeate compartment. In one embodiment, the width of atleast one channel 974 decreases by a factor greater than about two froman inlet of the channel 974 to an outlet of the channel 974. In oneembodiment, the width of at least one channel 974 decreases by a factorgreater than about four from an inlet of the channel 974 to an outlet ofthe channel 974 and additionally the channel has a dimensionless lengthgreater than about 2,000 and in another embodiment greater than about3,000, and in yet another embodiment greater than about 4,000.

Referring to FIG. 9B, in which like elements are provided having likereference designations as in FIG. 9A a permeate compartment 980 isformed with a permeate spacer 981 and a sealant forming shell 972. Thequantity, size and location of feed, retentate and permeate flowpassages, is based on multiple factors such as, for example, the desiredflow rates (which are in turn determined by the dimension of each stackand the number of stacks in each module), the desired location of thefeed, retentate and permeate ports of the module, and by desiredcleaning and purging considerations. The properties of the permeatespacer are selected, among other considerations, to minimize hold-upvolume, provide adequate support to the membrane and to preventexcessive pressure differentials within the permeate compartment. Thefeed compartment 970 of FIG. 9A is aligned with the permeate compartment980.

In operation, a feed stream is introduced into the feed compartment 970through the plurality of secondary flow passages 976, fed in turn byfeed primary flow passages 975, the latter can span the whole module andform a feed manifold for the module. The secondary flow passages 976introduce the feed stream into inlet end of the channel 974, inducingtangential flow in the channel 974. The tangential velocity of theliquid within the channel, represented by the arrows, remainssubstantially constant along the channel length by virtue of thediminishing channel width 979. Retentate exits the channel 974 throughthe secondary flow passages 977 located at the outlet end of the channel974, the secondary flow passages 977 further feeding retentate primaryflow passage 978 which can span the entire module 900 and forming aretentate manifold. The permeate stream enters a permeate compartment984 by permeating through a membrane (not shown) separating feedcompartment 970 from adjacent permeate compartment 980. Permeate can becollected by means of a plurality of permeate secondary flow passages983 which in turn feed permeate primary passages 982, which can span thewhole module forming a permeate manifold. The module 900 with combinedfeed compartment 970 and permeate compartment 980 operates in SPF modeas described above in conjunction with FIG. 2.

The length of the channel 974, in one example, is approximately 5 timesthe length of the module 900 by virtue of the multiple twists-and-turnsof the flow channel. Furthermore, channel width 979 diminishes byapproximately a factor of ten from the inlet to the outlet end of thechannel 974. The thickness and porosity of the feed spacer 971 affectthe void volume of the channel 974 and in one embodiment is such thatthe specific membrane area of the flow channel is greater than about 40cm⁻¹, in other embodiments greater than about 50 cm⁻¹, and in otherembodiments greater than about 130 cm⁻¹. Other types of membranes(flat-sheet, hollow fiber, monoliths) can be used to construct a modulesimilar to module 900. However, construction of such an element isfacilitated by the use of flat-sheet membranes, where a reduction incross-sectional area can more readily be obtained by reducing the widthof the rectangular channels along the flow path.

Referring to FIGS. 10A-10E, a spiral-wound separation module 1000 forthe filtration of liquids, having similar channel features as module 900of FIG. 9A, includes a spirally-wound membrane element 1002 coiledaround a center tube 1006. The spiral element 1002 is formed by stackinga membrane (not shown), a feed compartment 1030, another membrane (notshown) and a permeate compartment 1040, and then winding this four-layerlaminate around center tube 1006. In other words, one end of the centertube 1006 comprises primary and secondary flow passages 1019 and 1024,respectively, for the feed stream, whereas the other end comprisesprimary and secondary flow passages 1018 and 1028, respectively, for theretentate stream. The spiral-wound module 1000 further includes atubular shell 1008 forming a cylindrical housing with a feed port 1016on one end, a retentate port 1014 on the opposite end, and a permeateport 1012 on one side of tubular shell 1008. The center tube 1006 formsa coaxial retentate primary flow passage 1018 fluidly coupled to asecondary flow passage 1028 and forms a feed primary flow passage 1019fluidly coupled to secondary flow passages 1024. The feed primary flowpassage 1019 is disposed opposite the retentate primary flow passage1018 with the plug 1022 interposed between passages 1018 and 1019. Thespiral-wound module 1000 further includes a permeate collector 1010fluidly coupled to the permeate port 1012 disposed in the tubular shell1008. The tubular shell 1008 further includes seal 1020 disposedadjacent the feed port 1016 and an inlet end of the spiral element 1002and end cap 1026 disposed adjacent the retentate port 1014. In analternate embodiment, the location and orientation of the feed port1016, retentate port 1014 and permeate port 1012 can be differentaccording to the needs of the application. For example, the permeatecollector 1010 could be located on the same end as the feed port 1016 bychanging the location of the seals 1020 in the permeate compartment 1040as shown in FIG. 10C. In another alternative embodiment, ports 1012,1014 and 1016 can be located on the same end of the spiral-wound module1000 which adds flexibility in designing separation systems utilizingthese spiral-wound modules 1000 by placing all ports on the same end ofthe module. Referring again to FIG. 10B, the feed compartment 1030comprises a feed spacer 1031 and the seal 1020. Ribs 1033 are embeddedinto the feed spacer 1031 forming a channel 1004 having an inlet end, anoutlet end and a width 1039 which diminishes along the length of channel1004. Referring to FIG. 10C, the permeate compartment 1040 includes apermeate spacer 1042 and the seal 1020.

In operation, a feed stream is introduced into the feed compartment 1030through the plurality of secondary flow passages 1024, fed in turn byfeed primary flow passage 1019 coupled to the feed port 1016. Secondaryflow passages 1024 introduce the feed stream into the channel 1004,inducing tangential flow in the channel 1004. The tangential velocity ofthe liquid within the channel 1004, represented by arrows in FIG. 10B,remains substantially constant along the channel length by virtue of thediminishing channel width 1039. Retentate exits the channel 1004 throughsecondary flow passage 1028, which in turn fluidly connects into theretentate primary flow passage 1018, coupled to the retentate port 1014.In this embodiment, the length of the channel 1004 is approximately fourtimes the length of the feed compartment 1030 by virtue of the multipletwists-and-turns of the channel 1004. Furthermore, channel width 1039diminishes by approximately a factor of eight from the inlet end to theoutlet end of channel 1004. The thickness and porosity of the feedspacer 1031 is selected to provide a specific membrane area of thechannel 1004 greater than about 40 cm⁻¹, in other embodiments greaterthan about 80 cm⁻¹, and in other embodiments greater than about 50 cm⁻¹.In another embodiment, the specific membrane area of the channel 1004 isgreater than about 130 cm⁻¹ and the width of the channel 1004 decreasesby a factor greater than about two from the inlet of the channel 1004 tothe outlet of the channel 1004.

A permeate stream enters the permeate compartment 1040 by permeatingthrough the membrane separating the feed compartment 1030 from thepermeate compartment 1040. Permeate velocity increases along the flowpath as indicated by arrows, flowing to the end of the permeatecompartment where the permeate is collected in the permeate collector1010. The properties of the permeate spacer 1042 can be selected, forexample, to minimize hold-up volume, provide adequate support to themembrane and to prevent excessive pressure differentials within thepermeate compartment 1040. In an alternative embodiment, a retentateport can be provided on the same end as the feed port.

An alternate embodiment similar to spiral-wound separation module 1000shown in FIGS. 10A-E can be used to provide an internally-staged SPFmodule suitable for diafiltration. In this embodiment, multiple spiralcartridges similar to those described in above, are serially coupled,each spiral element forming one stage of the multi-stage module.Diafiltrate is then introduced and distributed to the inlet of eachstage by means of internal or external passageways. The diafiltrationpassageways are embedded within the center tube 1006 by means of acoaxial passageway concentric to the primary feed and retentatepassageways 1019 and 1018, respectively. In still another embodimentconventional spiral cartridges (not shown) instead of module 1000 areserially coupled to form a multi-stage module. In this case the centertube carries the permeate instead of carrying the feed and retentate.The diafiltrate is introduced and distributed to the inlet of each stageby means of internal or external passageways.

Referring now to FIG. 11A, a single pass filter system 1100 includes aplurality of stages 1102, 1104, and 1106, each stage having one or morecassettes 1110, a top plate 1112, a plurality of staging plates 1114 anda bottom plate 1116 in a stacked configuration. The cassettes 1110 eachhave at least one channel (not shown) fluidly coupled to a feed manifold1118, a retentate manifold 1119 and at least one permeate channel (notshown). The top plate 1112 includes a feed port 1120 in fluidcommunication with a feed pump 1122. The staging plate 1114 includes apass through port 1124 disposed to align with corresponding feedmanifolds 1118 and retentate manifolds 1119. The bottom plate 1116includes a retentate port 1142 in fluid communication with the retentatemanifold of the adjacent cassette 1110. The staging plates 1114 aredisposed to fluidly couple at least one retentate manifold from theupstream stage to the feed manifold of the adjacent stage downstreamthereby serializing the retentate flow while leaving the permeatechannels coupled in parallel. In other embodiments the permeate fromeach stage 1102-1106 is separately collected by means of a permeatedistributor. In one embodiment the cassettes 1110 are conventionalcassettes, for example GE 30 K polysulfone lab cassette Part#UFELA0030001ST; Pall Omega 10 KD T2 0.2 sq ft Centramate™ cassette;Millipore Pellicon 3 MicroCassette 10 K regenerated cellulose, CatalogNo. P3C 010C00. Although conventional cassettes can be used, separationperformance is enhanced by the use of cassettes having higher specificmembrane areas. In one embodiment, the system 1100 has a 3,2,1,1configuration (i.e., a stack including the top plate 1112, threecassettes 1110, staging plate 1114, two cassettes 1110, staging plate1114, one cassette 1110, staging plate 1114, one cassette 1110, and thebottom plate 1116).

In operation, the system 1100 runs as a single-pass process similar tothe process described in FIG. 2, and staging improves the performance ofthe separation process, including a flux enhancement. In each stage, forexample stage 1102, the feed manifolds 1118 of each cassette 1110 arefluidly coupled in parallel, however the staging plate 1114 blocks thefeed stream at point 1126 from entering the next stage 1104 as wouldoccur in a conventional plate and frame assembly thereby serializing theflow through the retentate manifolds 1119, the pass through port 1124 inthe staging plate 1114 and the feed manifolds 1118 in the cassettes 1110comprising the next stage 1104. In one embodiment, the specific feedflow rate for this staged system 1100 is about 112 lmh and thedimensionless length for the system is about 5,200. Here the SPFoperation with the low specific feed flow rate is enabled by theserialization of the channels of the cassettes 1110.

From the foregoing, it can be appreciated that the modules, systems andmethods of the invention facilitate SPF operation. The invention will befurther described in the following example, which is not exhaustive anddoes not limit the scope of the invention described in the claims.

EXAMPLE 1

In this example, a 1% solution of Bovine Serum Albumin in a pH 7.6phosphate diafiltrate was concentrated using cassettes comprisingmembrane with a MWCO of 10,000 Daltons arranged in a system similar tosystem 1100. The system included four stages connected in series usingstaging plates similar to staging plate 1114; the feed to an adjacentfollowing stage being the retentate of the adjacent preceding stage. Thefirst stage included four cassettes in parallel, the second had threecassettes in parallel, the third stage had two cassettes in parallel andthe fourth stage had a single cassette. Each cassette had a σ_(c) valueof about 70 cm⁻¹. The λ_(stage) values of the stages were about 1,300and by using the staging plates the λ_(system) value of the system wasabout 5,040. A peristaltic pump supplied feed solution to the firststage and a valve on the outlet of the last stage controlled theretentate flow rate. In a series of experiments conversions of between85% and 90% were achieved with fluxes of between 74 to 127 lmhcorresponding to specific feed rates in the range of 81 to 140 lmh.These tests showed that it is possible to achieve high conversions, in asingle pass, without needing to recirculate retentate to the feed. Thecombination of a high σ_(c) value in combination with a maximumλ_(stage) value and a minimum value of λ_(system) makes possible theconcentration or diafiltration of solutions at attractive fluxes and lowdiafiltration requirements when used for diafiltration.

Referring now to FIGS. 11B and 11C, in which like elements are providedhaving like reference designations as in FIG. 11A, the staging plate1114 includes a pass through port 1124 and a plurality of permeate ports1130. The standard lab-scale cassette 1110 includes a pair of feedpassages 1134 and 1136 and a pair of permeate passages 1132. When thecassette 1110 is stacked adjacent the staging plate 1114, feed passage1134 is blocked by the staging plate 1114 which in operation essentiallyserializes the flow by forcing the retentate from the cassettes 1110 aswell as any additional cassettes 1110 stacked adjacent the cassette 1110adjacent the staging plate 1114 to provide the feed to the followingadjacent stage. The resulting flow path, represented by arrows, is shownin FIG. 11D.

The embodiment represented in FIG. 11D is an internally-staged modulewith a 3-2-1-1 configuration. This module effectively comprises threestages, the first and second stages having λ_(stage) values of 1300,while the third stage has a λ_(stage) value of 2600, resulting in aλ_(system) value for the module of 5200. The last two cassettes 1110 andstaging plate 1114 comprise a single stage 1106 because there is nophysical property change and no stage transition between the twocassettes 1110 in stage 1106. In alternative embodiment similar tosystem 1100 of FIG. 11D, the system also has a 3-2-1-1 configuration andadditionally includes a permeate distributor to control the permeatepressure in each stage at a predetermined value, In contrast to system1100 this system has 4 stages, each stage having the same value ofλ_(stage) of about 1300.

Referring now to FIG. 11D, in which like elements are provided havinglike reference designations as in FIGS. 11A, 11B and 11C, the flow pathsthrough system 1100 are shown. The feed stream flows through and entersthe feed port 1120 of the top plate 1112. The feed stream then flows inparallel into the feed manifold 1118 of each cassette 1110. The feedstream then flows across the channel as indicated by arrow 1144 andflows into the retentate manifold 1119 of each cassette 1110 asindicated by flow arrows 1146. The retentate output of stage one thenflows through the pass through port 1124 of the staging plate 1114 intothe cassettes 1110 of stage two as indicated by flow arrows 1148. Notethat at section 1126 of the staging plate 1114 the normally parallelfeed flow is blocked. The flow continues in a similar manner until theflow reaches the bottom plate 1116 and the retentate exits through theretentate port 1142 as indicated by flow arrow 1166.

A comparison between a conventional batch TFF concentration process andthe SPF concentration process obtained in a system similar to system1100 is listed in Table 2. It is noted that although the process time isequivalent, the capital costs and the holdup volumes are much larger forthe conventional batch system.

TABLE 2 Batch vs. SPF Concentration System 12,000 liters concentrated to500 liters BATCH SPF Membrane Area [m²] 40 40 Process Time [hr] 4 4 PumpCapacity [L/hr] 14,000 3,000 Recirculation Loop YES Not Needed No. ofPump Passes 10–100 1 Relative Holdup Volume 4 1 Relative Capital Cost2.5 1 Feed Tank YES Not Needed Heat Exchanger Possibly Needed Not Needed

Now referring to FIG. 12, a graph of flux as a function of TMP forsystem 1100 of FIG. 11A is shown. Curve 1200 represents the average fluxas a function of TMP measured with conversion set and maintained at 90%.The average flux was calculated by measuring the total permeation rate(i.e., for the four stages) and dividing it by the total membrane areafor the stages of system 1100. The flux vs. TMP response is quitedifferent from that obtained with conventional TFF. Conventional TFF issometimes characterized by a maximum flux or a plateau that occurs athigh values of TMP. In contrast, no such plateau is present in constantconversion SPF mode because an increase in TMP simultaneously results inan increase in cross-flow rate, which in turn increases the permeationcapability of the module. Unlike some conventional TFF concentrationprocesses, which attempt to maintain a constant TMP throughout the flowpath, the improved SPF concentration process operates with amonotonically decreasing TMP (e.g., the highest TMP at the inlet and adecreasing TMP along the flow path).

Now referring to FIG. 13A, an internally-staged diafiltration system1300 according to the invention includes diafiltration module 1301having a plurality of stages 1302 a-1302 m (collectively referred to asstages 1302), each stage having a plurality of channels 1304. The stages1302 are disposed such that each stage 1302 is in fluid communicationwith each adjacent stage 1302 preceding it and is in fluid communicationwith each adjacent stage 1302 that follows it. Each of the channels 1304includes a filtration membrane (not shown). As described above, each ofthe channels 1304 has a length, a membrane area, a void volume, aspecific membrane area expressed as a ratio of the membrane area to thevoid volume, and a dimensionless length expressed as a product of thechannel length and the specific membrane area. The system 1300 furtherincludes a diafiltrate source 1308 fluidly coupled to a pressure source1312 which is fluidly coupled to at least one diafiltration distributor1309 having a network of diafiltration flow passages 1310 a-1310 m withpredetermined hydraulic resistances which are in turn fluidly coupled tocorresponding manifolds 1306 which are fluidly coupled to correspondingstages 1302. It is understood that the number of channels 1304 in eachstage 1302 could differ, the channels 1304 could be identical or couldhave different properties, each stage 1302 does not require connectionto one of the diafiltration flow passages 1310, and that not every stage1302 receives diafiltrate.

In operation, diafiltrate is introduced under pressure provided by thepressure source 1312 through the diafiltration flow passages 1310 of thediafiltration distributor 1309 and the manifolds 1306 into the channels1304 of the stages 1302. The diafiltration process is operated as an SPFprocess similar to the process described in FIG. 2. In one embodimentthe stages 1302 and channels 1304 are substantially identical and thepressure source 1312 is an external pump. SPF operation is provided inthis embodiment by selecting a purification factor for the process andadjusting at least one of the diafiltration flow rate, the feed flowrate and the retentate flow rate until the desired purification isobtained. Table 3 shows a comparison between a conventionaldiafiltration process and a diafiltration process using a system similarto system 1300 operating in an SPF mode. Additional details of theintroduction of the diafiltrate are described in conjunction with FIG.13B. Generally the diafiltration stages 1302 are similar andcorrespondingly equal diafiltration rates are used for each stage 1302.However, in other embodiments combining concentration and diafiltration,stages may have different membrane areas, different numbers of channels(e.g., a 4-3-2-1 configuration) and different values of σ_(c), and thediafiltrate may be supplied to selected stages at different rates.

Referring to FIG. 13B, an internally-staged diafiltration module 1318similar to the diafiltration module 1301 in FIG. 13A includes aplurality of stages 1322 a-1322 m (collectively referred to as stages1322), each stage having a plurality of channels 1324. Each channel 1324comprises a membrane 1326 disposed adjacent to a feed spacer 1328 whichprovides support for the membrane 1326. In one embodiment, the channels1324 have σ_(c) values of greater than about 40 cm⁻¹ and λ_(stage)values of less than about 6,000. In this embodiment, the λ_(system)(i.e., the λ of the module) for module 1318 is greater than 2,000. Themodule 1318 further includes feed manifolds 1330 and retentate manifold1332 fluidly coupled to the channels 1324 of the each stage 1322. Boththe feed manifold 1330 and the retentate manifold 1332 have a primaryflow passage 1323 and secondary flow passages 1325. The stages 1322 aredisposed such that each stage is in fluid communication with eachadjacent stage 1322 preceding it and is in fluid communication with eachadjacent stage 1322 that follows it. The module 1318 further includesinlet port 1344 fluidly coupled to the feed manifold 1330 of stage 1322a and a retentate outlet port 1340 fluidly coupled to the last stage1322 m. The module 1318 further includes a diafiltration distributor1350 which comprises a plurality of diafiltration flow passages 1352a-1352 k (collectively referred to as diafiltration flow passages 1352)and a diafiltrate inlet port 1342 fluidly coupled to the diafiltrationflow passage 1352 a. The diafiltration distributor 1350 furthercomprises a plurality of diafiltration passageways 1354 fluidly couplingrespective diafiltration flow passages 1352 to the corresponding feedmanifolds 1330. The diafiltration flow passages 1352 include diafiltratespacers 1356 having predetermined hydraulic resistances so as tointroduce diafiltrate at a predetermined flow rate at a selectedpressure into corresponding feed manifolds 1330.

In one embodiment, the diafiltration flow passages 1352 having apredetermined hydraulic resistance are formed with the spacers 1356configured and stacked by means similar to those used for making thechannels 1324. The hydraulic resistance of the diafiltration flowpassage 1352 is a function of (a) the hydraulic diameter of the spacer1356, (b) the width of the channel formed by the spacer 1356, and (c)the effective path length of the spacer 1356. The determination of thehydraulic resistance values is described in more detail in conjunctionwith FIGS. 14A, 14B and 15.

In operation, a feed stream flows through primary flow passage 1323 inthe feed manifold 1330 of the first stage 1322 a, which in turn feedssecondary flow passages 1325 which feeds channels 1324 of first stage1322 a. The retentate from the channels 1324 are collected throughsecondary flow passages 1325, which feed primary flow passage 1323 ofthe retentate manifold 1332 of the first stage 1322 a. Diafiltrationsolution is introduced into diafiltrate flow distributor 1350 throughthe diafiltrate inlet port 1342 and into the diafiltration flow passage1352 a. Diafiltration distributor 1350 allows a predetermined fractionof the diafiltration stream to enter the feed manifold 1330 at a pointupstream of secondary flow passages 1325 to promote the mixing of thediafiltrate with the feed stream before the diafiltrate enters channels1324. The hydraulic resistance of the diafiltrate spacer 1356 inaddition to the external pressure source controls the hydraulic pressureof the diafiltrate stream along the diafiltration flow passages 1352 inorder to control the introduction of diafiltrate into the feed manifold1330 of each stage 1322. In certain embodiments the diafiltration flowpassages 1352 have differing hydraulic resistances.

In alternative embodiments, the inlet port 1344 and the retentate outletport 1340 can be located in different places in the housing 1320according the application requirements. In one embodiment, the module1318 has ports 1340, 1342 and 1344 located on one face of the module, toconveniently facilitate the installation and replacement of each modulein a separation system (not shown). The routing and location of theprimary and secondary flow passages will be dictated by manufacturingconsiderations known to those skilled in the art. Limiting the value ofλ_(stage) results in the use of a larger number of stages for a givendegree of impurity removal results in a lower consumption ofdiafiltrate. In one embodiment, the module 1318 includes an optionaldiafiltration spacer (not shown) disposed in the diafiltration flowpassage 1352 providing a hydraulic resistance predetermined to furthercontrol the flow rate of a diafiltrate along the diafiltration flowpassage 1352. A comparison between a conventional batch TFFdiafiltration process and the SPF diafiltration process obtained using asystem similar to system 1300 is listed in Table 3.

TABLE 3 Batch vs. SPF Diafiltration System - 1,000 liters diafiltrated100-fold BATCH SPF Membrane Area [m²] 15 15 Process Time [hr] 4 4 PumpCapacity [L/hr] 5,300 250 Recirculation Loop Needed Not Needed No. ofPump Passes 20 or more 1 Diafiltrate Volume [L] 4600 4600 DiafiltrateVolume Not practical 3,800 with counter flow of diafiltrate InternalStages 1 10 Relative Holdup Volume 4 1 Relative Capital Cost 2.5 1 FeedTank Needed Not Needed Heat Exchanger Needed Not Needed

The effect of the diafiltration process is to wash (i.e., purify) theretentate stream solution in an in-line fashion along the flow path. Thechannels in the four stages 1322 are included within a singleinternally-staged module. For example, if each stage provides 80%conversion, and one part of the retentate from each stage is dilutedwith about four parts of diafiltrate, the internally-staged module 1320will remove low molecular weight impurities by almost 625-fold, apurification equivalent to a “6.44-volume” batch diafiltration process.

In the staged diafiltration module using a common source of diafiltrate,it is possible to distribute the diafiltrate to selected stages 1322 byproviding the passive distributor 1350 including the network ofdiafiltration flow passages 1354 interposed between the common source ofdiafiltrate and the inlet of each selected stage 1322. The diafiltrationflow passages 1354 of the diafiltration distributor 1350 have hydraulicresistances that result in a specified flow rate of diafiltrate to eachselected stage 1322. Since the pressure at the inlet of each selectedstage 1322 decreases in the direction of the feed flow, the hydraulicresistance of the each of the diafiltration flow passages 1354 needs toincrease from stage to stage in the direction of flow in order todeliver a desired amount of diafiltrate in each stage 1322. For anygiven diafiltration pressure to the staged array and a given retentatepressure at the retentate of the staged array it is possible to specifythe hydraulic resistance of each diafiltration flow passage 1354 inorder to achieve a desired diafiltration rate to any selected stage 1322even if the diafiltrate source is at a pressure different from thepressure at the inlet to one of the selected stages 1322.

In one embodiment, the internally-staged diafiltration module 1318receives diafiltrate at a feed flow rate to the staged array equal tothe retentate flow rate from the module 1318. Operating with thisembodiment, the diafiltration flow rate to each stage should preferablybe the same. This equality of diafiltrate flow rate can be arranged byproviding suitable hydraulic resistances for each diafiltration flowpassage 1352 of the distributor 1350, based on a known pressure at theinlet of each stage 1322. Should there be a deviation in the value ofthe pressures at the feed manifold 1330 of the stage 1322, thediafiltration flow rate to that stage 1322 may become greater or lessthan the diafiltration flow rate to other stages. This is an undesirablesituation because unequal flow rates of diafiltrate to stages 1322 canresult in an increase in the total volume of diafiltrate to achieve agiven degree of impurity removal, which the diafiltration process isdesigned to achieve and can also result in overconcentration of thedesired solute at one of the stages within the module. This undesirableeffect can be mitigated when using a diafiltration distributorcomprising a parallel network of resistors by supplying the diafiltrateat source pressure considerably higher than the pressures prevailing inthe staged module 1318. This results in the distribution of diafiltrateamong the stages 1322 being less sensitive to possible variations in thestage inlet pressures. The hydraulic resistances of the individualdistributors are arranged to provide the desired diafiltrate flow rateto each stage, based on the value of the pressure of the commondiafiltrate source. In one embodiment the diafiltrate is supplied tocorresponding stages at a source pressure greater than about one and onehalf times the feed pressure to module 1318 such that the effect ofvarying channel pressures on diafiltrate flow rate are reduced. Inanother embodiment the diafiltrate is supplied to corresponding stagesat a source pressure of about 10 psi greater than the feed pressure tomodule 1318 such that the effect of varying channel pressures ondiafiltrate flow rate are reduced.

It will also be appreciated that the diafiltration process can beoperated in a counter current mode by fluidly coupling a permeatechannel to at least one preceding flow channel. A counter currentdiafiltration module would be similar to module 1318 further including adiafiltration distributor but with a permeate compartment from at leastone stage providing the source of diafiltrate to a preceding stage. Apump is needed to increase the pressure of the permeate to the pressureof said receiving flow channel as illustrated in FIGS. 15 and 20. TheSPF diafiltration module with counter current diafiltration modulegenerally reduces the quantity of fresh diafiltrate required for theprocess.

FIG. 14A, 14B and 14C, in which like elements are provided having likereference designations throughout the several views, illustrateexemplary resistive models of the of the diafiltration distributor 1309hydraulic resistances provided by the individual flow channels 1310 ofFIG. 13A. Referring to FIG. 14A, an exemplary module 1400 withcomponents shown as a resistive network includes a plurality of stages1402 a-1402 n each having a retentate output 1404, a feed input 1406 anda permeate output 1408. The module 1400 further includes at least onediafiltration distributor 1416 having a plurality of diafiltration flowpassages 1414 a-1414 m which are fluidly coupled to a pressurizeddiafiltrate source 1412. Resistances 1410 a-1410 m represent thepredetermined hydraulic resistance of the corresponding diafiltrationflow passages 1414 coupled in a parallel network and are used to controlthe flow rates of diafiltrate streams being fed to each stage receivingdiafiltrate. The diafiltration flow passages 1414 fluidly couple thediafiltrate source 1412 to the corresponding feed input 1406 to eachstage receiving diafiltrate.

The predetermined resistances of the diafiltration flow passages 1414are based on the pressures prevailing in the feed to the various stagesand the desired diafiltrate flow rate to each stage. A predeterminedrange of diafiltration supply pressures is selected to make thediafiltrate flow rate to each stage receiving diafiltrate insensitive tothe variations in the feed pressures in those stages. The resistances ofthe diafiltration flow passages 1414 are formed physically, for example,by varying diameter and length of the diafiltration flow passages in anexternally staged module or by providing channels having varying crosssections, by varying the hydraulic diameter of the diafiltration flowpassages 1414, or by introducing orifices within the diafiltration flowpassages 1414.

The resistive values are predetermined by modeling the performance ofthe system (e.g., numerically or using computer simulation) or can bedetermined empirically. In one embodiment values of the individualparallel resistances in module 1400 are chosen to add a substantiallysimilar diafiltrate flow rate to each stage although the pressure at theinlet to the stage varies. Generally, larger values of hydraulicresistance are provided for downstream stages. In addition, supplyingthe diafiltrate at a substantially higher pressure than the feedpressures to the stages reduces the effect of varying channel pressureson diafiltration flow rates. In one embodiment the diafiltrate pressureis supplied to selected stages at a source pressure greater than aboutone and one half times the feed pressure to the module 1400 so theeffect of varying feed pressures on diafiltrate flow rate is reduced. Inanother embodiment the diafiltrate pressure is supplied to selectedstages at a source pressure of about 10 psi greater than the feedpressure to the module 1400.

Now referring to FIG. 14B, an exemplary module 1400′ includes at leastone diafiltration distributor 1416′ having a plurality of diafiltrationflow passages 1420 a-1420 m which are fluidly coupled to the pressurizeddiafiltrate source 1412. Resistors 1422 a-1422 m represent thepredetermined hydraulic resistance of the corresponding diafiltrationflow passages 1414 coupled in a series network and are used to controlthe flow rate of a diafiltrate stream to each stage 1402. Thediafiltration flow passages 1420 fluidly couple the diafiltrate source1412 to the corresponding feed input 1406 of each stage receivingdiafiltrate. The diafiltration distributor 1416′ is similar to theseries diafiltration distributor 1309 of FIG. 13A. A benefit of theseries configuration is the ease of integration in some embodiments ofSPF modules and systems. One benefit of the parallel configuration isthat any partial blockage of a channel has less impact on theperformance of the entire distributor, and the parallel configurationfacilitates the use of higher diafiltrate source pressures to reduce thesensitivity of the performance of the distributor to variations in feedpressures to the stages.

Now referring to FIG. 14C, an exemplary module 1400″ includes at leastone diafiltration distributor 1416″ having a plurality of diafiltrationflow passages 1420 a′-1420 m′ which are fluidly coupled (sometimesthrough the corresponding resistor) to the pressurized diafiltratesource 1412. Resistors 1422 a′-1422 m′ and 1410 a′-1410 m′ represent thepredetermined hydraulic resistance of the corresponding diafiltrationflow passages 1414 coupled in a series-parallel network and are used tocontrol the flow rate of each diafiltrate stream. The diafiltration flowpassages 1414 and 1420′ fluidly couple the diafiltrate source 1412 tothe corresponding feed inputs 1406 to each stage. One method ofimplementing the diafiltration distributor in an externally stagedsystem is to use tubing with the hydraulic resistance being provided bythe length and diameter of each tubing section. The series-parallelconfiguration combines some of the features of the series and parallelconfigurations at the cost of some additional complexity.

Referring to FIG. 15, a counter current diafiltration module 1500according to the invention includes components having hydraulicproperties shown as a resistive network. The module 1500 includes aplurality of stages 1502 a-1502 n each having a retentate output 1504, afeed input 1506 and a permeate output 1508. The module 1500 furtherincludes at least one diafiltration distributor 1516 similar to thediafiltration distributor 1416 of FIG. 14A and a pressurized diafiltratesource 1512. The module 1500 further includes at least one countercurrent diafiltration distributor 1522 and a pump 1520 fluidly coupledto a one or more permeate outputs 1508 supplying the permeate as adiafiltrate source. Resistors 1510 a-1510 b represent the predeterminedhydraulic resistance of the corresponding counter current diafiltrationflow passages 1514 a-1514 b coupled in a parallel network and are usedto control the flow rate of the counter current diafiltrate stream toeach stage. The pump 1520 is used to raise the pressure of the permeatefrom one or more stages 1502, here stages 1502 d and 1502 n, to besupplied as the diafiltrate to one or more preceding stages, here stages1502 b and 1502 c. The counter current diafiltration distributor 1522provides diafiltrate from following stages to channels in precedingstages. In one embodiment, diafiltrate is optionally added to the firststage 1502 a (not shown).

Referring to FIG. 16A an internally staged hollow fiber module 1600includes a plurality of annular stages 1610 a-1610 c (collectivelyreferred to as stages 1610) disposed within a cylindrical housing 1602,also referred to as a hollow fiber cartridge, having an upper end cap1608 and lower end cap 1609. Each stage 1610 includes a plurality ofchannels, here hollow fiber membranes 1620 (also referred to as hollowfibers 1620), and the number of hollow fiber membranes 1620 can be thesame in each stage 1610 or can be different as shown in FIG. 16A. In oneembodiment the hollow fibers 1620 are disposed in an annular ring aroundan axis of the module 1600 forming a cylinder as shown in more detail inconjunction with FIG. 16B. The module 1600 further includes a pluralityof cylindrical flow diverters 1604 a-1604 b (collectively referred to ascylindrical flow diverter 1604) disposed within the upper and lower endcaps 1608, 1609, substantially parallel to the hollow fiber membranes1620 and segregating the hollow fiber membranes 1620 so as to form thestages 1610, an inlet port 1606 disposed in the housing, a retentateport 1616 disposed in the housing and a permeate port 1612 disposed inthe housing. In one embodiment, flow diverters 1604 form a fluid sealwith a tube sheet (not shown) attached to the hollow fiber membranes1620 within the upper and lower end caps 1608, 1609. In anotherembodiment, each of the channels, here the hollow fiber membranes 1620,has a dimensionless length, λ_(stage), lower than about 6,000 a specificmembrane area greater than about 50 cm⁻¹, and a dimensionless length,λ_(system), for the module of at least about 2,000.

In operation, the hollow fiber membranes 1620 are arranged as acylinder, and in the embodiment of FIG. 16A are divided into four stages1610 by the cylindrical flow diverters 1604. A feed enters the outermoststage 1610 a through the inlet port 1606, and flows through the lumensof the hollow fiber membranes 1620 as shown by flow path 1624. The feedstream enters a bottom section of stage 1610 a, and then is directed inupward flow by the cylindrical flow diverters 1604 a, into the second,middle, stage 1610 b. On leaving the middle stage 1610 b, in the uppersection of the module 1600, the flow is diverted downward through theinner most, cylindrical, stage, 1610 n. The retentate is directed out ofthe module 1600 through retentate port 1616. The permeate from the threestages 1610 exits the module 1600 through the permeate port 1612. Thehollow fiber membranes 1620 are coupled together and the module 1600includes seals (not shown) using hollow fiber encapsulation techniquesknown in the art to separate and fluidly couple the stages 1610.

Referring to FIG. 16B, in which like elements are provided having likereference designations as in FIG. 16A, the internally staged hollowfiber module 1600 shown in cross section along the axes of the hollowfiber membranes 1620 includes the cylindrical flow diverters 1604dividing the hollow fiber membranes 1620 into stages 1610. The “X” 1635indicates a flow directed into the page and the dot 1637 indicates flowout of the page illustrating that the flow in the hollow fiber membranes1620 alternates direction in adjacent stages 1610. The module 1600 canbe manufactured using techniques known in the art including end caps andtube sheets and other arrangements described in conjunction with FIG.18A. Other embodiments of internally staged modules, comprising hollowfiber membranes in which the feed and retentate flow though the lumen ofthe hollow fibers, can be configured in various topologies. For example,the individual stages can be arranged in the form of cylindrical discs,within a cylindrical housing. The feed and retentate flows are in theaxial direction from one stage to the next stage. It is also possible toarrange the individual stages in the form of sectors within acylindrical housing. A feed stream enters a first sector and theretentate from the module leaves from the last sector. Such a deviceincludes suitable passageways to conduct the retentate from one sectorto the feed port of the next sector.

Referring to FIG. 17, in which like elements are provided having likereference designations as in FIG. 16A, a hollow fiber module 1600′similar to module 1600 in FIG. 16A with the addition of at least onediafiltration distributor 1628 fluidly coupled to a pressurized sourceof diafiltrate 1630. The diafiltration distributor 1628 includesdiafiltration flow passages 1631 and 1632. In one embodiment the stages1610 a′-1610 n′ (collectively referred to as stages 1610′) aresubstantially identical having the approximately the same number ofhollow fiber membranes 1620 unlike the stages 1610 in FIG. 16A. Themodule 1600′ includes a plurality of cylindrical flow diverters 1604a′-1604 b′ (collectively referred to as cylindrical flow diverter 1604′)disposed within the housing substantially parallel to the hollow fibermembranes 1620 and segregating the hollow fiber membranes 1620 so as toform the stages 1610′.

In operation, the diafiltration distributor 1628 is connected to theinlet of the stages 1610′. The diafiltrate to the first stage 1610 a′flows through diafiltration flow passage 1631, to the second stage 1610b′ through diafiltration flow passages 1632 and to the third stage 1610n′ through diafiltration flow passages 1633. It will be appreciated thatalternative embodiments could supply diafiltrate to less than all thestages 1610′. In one embodiment, diafiltration flow passage 1631 haspredetermined hydraulic resistances to provide an approximately equalamount of diafiltrate to compensate for stage pressures variations.

Now referring to FIG. 18A, an alternative internally staged hollow fibermodule 1800 suitable for diafiltration according to the inventionincludes a plurality stages 1810 a-1810 n (collectively referred to asstages 1810) disposed within a cylindrical housing 1802. Each stage 1810includes a plurality of hollow fiber membranes 1820, and the number ofhollow fiber membranes 1820, here, are the same in each stage 1810. Inone embodiment the hollow fiber membranes 1820 are disposed in anannular ring (shown more clearly in FIG. 18B) forming a cylinder. Thehollow fiber membranes 1820 are joined and segregated in one embodimentby a tube sheet 1819 formed using potting compounds as is known in theart so as to form the stages 1810. The module 1800 further includes afeed port 1804 disposed in the housing 1802, a retentate port 1812disposed in the housing 1802, permeate perforations 1828 and a permeateport 1816 disposed in the housing 1802. The permeate perforations 1828are disposed to direct the permeate to the permeate port 1816. In oneembodiment, each of the stages 1810, here comprising the hollow fibermembranes 1820, has a dimensionless length, λ_(stage), less than about6,000, hollow fibers with specific membrane areas greater than about 50cm⁻¹, and a dimensionless length of the module 1800, λ_(system), greaterthan about 2,000.

The module 1800 further includes further includes a diafiltrationdistributor 1834 which comprises a diafiltration flow passage 1824 and adiafiltrate inlet port 1806 fluidly coupled to the diafiltration flowpassage 1824. The diafiltration distributor 1834 further comprises aplurality of diafiltration passageways 1822 fluidly coupling thediafiltration flow passage 1824 to the corresponding stages 1810. Thediafiltration flow passage 1824 includes a plurality of hydraulicresistors 1830 providing predetermined hydraulic resistances so as tointroduce diafiltrate at a predetermined flow rate at a selectedpressure into corresponding stages 1810. Now referring to FIG. 18B, inwhich like elements are provided having like reference designations asin FIG. 18A, the internally staged hollow fiber module 1800 furtherincludes an annular center core 1838 comprising a plurality of radialsupports 1840 coupled to an inner annular support ring 1842 around whichthe hollow fibers 1820 are disposed. The center core 1838 and thesupport ring 1842 extend axially along the module 1800. The perforations1828 are disposed in the inner annular support ring 1842. The housing1818 further comprises an outer shell 1844, and the hollow fibers 1820are disposed between the outer shell 1844 and the inner annular supportring 1842. In one embodiment, the hydraulic resistors 1830 comprise aporous plug, and the housing 1818, supports 1840, the outer shell 1844and the inner annular support ring 1842 are formed by an extrusionprocess as is known in the art.

In operation, diafiltrate is added via the diafiltration flow passages1824 of the diafiltration distributor 1834. The hydraulic resistors 1830provide the predetermined hydraulic resistance of the correspondingdiafiltration flow passage 1824 similar to the SPF operation of themodule 1318 of FIG. 13B. The diafiltration flow is terminated by plug1832 in the last stage 1810 n. The permeate is collected in the spacebetween the hollow fibers 1820 and flows through the perforations 1828to the permeate port 1816. The feed/retentate flows through the lumensof the hollow fibers 1820 in each stage 1810 after mixing with thediafiltrate and finally flows out the retentate port 1812.

Referring to FIG. 19A, a single pass diafiltration system 1900 includesa plurality of stages 1902, 1904, 1906, and 1908 each stage having oneor more cassettes 1910, a top plate 1912, a plurality of staging plates1914 and a bottom plate 1916 in a stacked configuration. The cassettes1910 each have at least one flow channel (not shown) fluidly coupled toa feed manifold 1918, a retentate manifold 1919 and at least onepermeate channel (not shown). The top plate 1912 includes a feed port1920 in fluid communication with a feed pump 1922 and a diafiltrationdistributor 1936 fluidly coupled to the feed inlet port 1920. Thestaging plate 1914 includes a pass through port 1924 disposed to alignwith corresponding feed manifolds 1918 and retentate manifolds 1919. Thestaging plate 1914 also includes a diafiltration distributor 1936fluidly coupled to the pass through port 1924. The bottom plate 1916includes a retentate port 1942 in fluid communication with the adjacentcassette 1910. The staging plates 1914 are disposed to serialize theretentate flow while leaving the permeate channels coupled in parallel.In one embodiment the cassettes 1910 are conventional cassettes similarto the cassettes used in system 1100 in FIG. 11A. Although conventionalcassettes can be used, performance is enhanced by the use of cassetteswith higher specific membrane areas.

In one embodiment, the system 1900 has a 2,2,2,2 configuration (i.e., astack including the top plate 1912, two cassettes 1910, staging plate1914, two cassettes 1910, staging plate 1914, two cassettes 1910,staging plate 1914, two cassettes 1910, and the bottom plate 1916). Inthis embodiment, the effect of staging is to enable diafiltration withflux and buffer consumption comparable to batch diafiltration.

In operation, the system 1900 runs as an SPF process similar to theprocess described in FIGS. 2, 11A and 13A. In each stage 1902, 1904 and1906, for example stage 1902, the feed manifolds 1918 of each cassette1910 are fluidly coupled in parallel however the staging plate 1914blocks the feed stream at point 1926 from entering stage 1904 as wouldoccur in a conventional plate and frame assembly thereby serializing theflow through the retentate manifolds 1919 and the pass through port 1924in the staging plate 1914. Here the low specific feed flow rate isenabled by the serialization of the flow channels of the cassettes 1910.In addition, diafiltrate is added at each stage in a process similar tothe process described above in conjunction with FIGS. 13A and 13B. Herehowever the diafiltrate is added through the feed port 1920 in the firststage 1902 and through the pass through port 1924 in the other stages1904, 1906 and 1908. Diafiltrate is optionally added to the first stage1902.

Referring to FIG. 19B, in which like elements are provided having likereference designations as in FIG. 19A, the flow paths through system1900 are shown. The feed stream flows through and enters the feed port1920 of the top plate 1912. The feed stream then flows in parallel intothe feed manifold 1918 of each cassette 1910. The feed stream then flowsacross the channel as indicated by flow arrow 1944 and flows into theretentate manifold 1919 of each cassette 1910 as indicated by flow arrow1946. The retentate of stage one then flows through the pass throughport 1924 of the staging plate 1914 into the cassettes 1910 of stage twoas indicated by flow arrow 1948. The diafiltrate is added into the passthrough port 1924 of distributor 1936 as indicated by flow arrow 1970.Note that at section 1926 of the staging plate 1914 the feed manifold ofthe first stage 1906 is blocked. The flow continues in a similar manneruntil the flow reaches the bottom plate 1916 and the retentate exitsthrough the retentate port 1942 as indicated by flow arrow 1966. It isunderstood that the system 1900 can include fewer or more than fourstages and that diafiltrate can be added at some or all the stages.

Now Referring to FIG. 20, a staged counter current diafiltration module2000 according to the invention includes a plurality of stages 2010a-2010 n (collectively referred to as stages 2010) each of the stages2010 having a plurality of channels 2004 and a plurality of permeatecompartments 2014 fluidly coupled to permeate distributor 2002 a and2002 b (collectively referred to as permeate distributors 2002).Permeate distributor 2002 b is fluidly coupled to a pressure source 2012which is fluidly coupled to a feed manifold 2006 a. Diafiltrationpassageways connecting the pressure source 2012 to the feed manifold2006 a are arranged to insure good mixing.

In operation, the permeate distributor 2002 b provides diafiltrate fromstage 2010 b to the preceding stage 2010 a. In other embodiments, thecounter current diafiltration module can include more than one permeatedistributor 2002, and the permeate distributor can combine the outputfrom one or more permeate compartments 2014. Furthermore, each permeatedistributor 2002 can supply diafiltrate to one or more stages 2010. Apressure source, for example, a pump, is provided for each permeatedistributor 2002 and corresponding counter current diafiltrationnetwork.

Referring now to FIG. 21, an internally staged SPF system 2100 withpermeate control according to the invention, includes a plurality ofstages 2110 a-2110 n (collectively referred to as stages 2110) each ofthe stages 2110 having a plurality of channels 2106 and a plurality ofpermeate compartments 2108 fluidly coupled to a permeate distributor2102. Each channel 2106 comprises a membrane 2126 disposed adjacent to afeed spacer 2128 which provides support for the membrane 2126. In oneembodiment, the channels 2106 have σ_(c) values of greater than about 40cm⁻¹ and the stages 2110 have λ_(stage) values of less than about 6,000.In this embodiment, the λ_(system) for system 2100 is greater than2,000. The permeate distributor 2102 includes a plurality of permeatemanifolds 2114 fluidly coupled to the plurality of permeate compartments2108 through a plurality of permeate flow passages 2118. The permeatedistributor 2102 further includes a permeate outlet port 2104 coupled tothe permeate manifold 2114 of the last stage 2110 n. The permeatedistributor 2102 further includes a permeate collector (not shown)fluidly coupled to the permeate outlet port 2104. The permeatedistributor 2102 provides a network of hydraulic resistors analogous tothe diafiltration distributor networks of modules 1400 and 1400′described in conjunction with FIGS. 14A and 14B.

The stages 2110 are disposed such that each stage is in fluidcommunication with each adjacent stage preceding it and is in fluidcommunication with each adjacent stage that follows it (i.e. theretentate from the i^(th) stage feeds the feed of the (i+1)^(th) stage).Each of the channels 2106 includes a filtration membrane. As describedabove, each of the channels 2106 has a length, a membrane area, a voidvolume, a specific membrane area expressed as a ratio of the membranearea to the void volume, and a dimensionless length expressed as aproduct of the channel length and the specific membrane area.

In operation, the predetermined hydraulic resistances of the flowpassages 2118 of the permeate distributor 2102 provides a pressure inthe permeate compartments 2108 of each stage thereby providing a targetTMP in the channels 2106 of each stage 2110, which in turn provides apredetermined permeation rate in each stage 2110. In one embodiment, itis desirable to maintain the same TMP in the channels 2106 of each stage2110 in spite of the fact that the feed pressure in each stage 2110decreases along the flow path. In this manner the TMP along the wholeflow path remains approximately constant in spite of the long flow path.In another embodiment, the predetermined permeation rate decreasesmonotonically from the first to the last stage. While the feed pressure,and therefore the TMP naturally decreases along the flow path, thepermeate distributor 2102 enables the control of the TMP in apredetermined manner independently of the pressure drop occurring in thechannels 2106. Controlling the TMP in the upstream stages to valueslower than what would be obtained without a permeate distributorprevents the over concentration of solute and thereby a more effectiveseparation process. In still another embodiment, high inlet feedpressures are used while controlling the TMP below a desired value bymeans of the permeate distributor 2102; in this manner very longchannels 2106 are used without incurring in excessive TMP anywhere inthe flow path.

In general, TMP control by means of the permeate distributor 2102provides an additional degree of freedom in the design of SPF modulesand processes to meet the needs of differing applications, for example,different concentrations and viscosities. Advantages in operating in SPFmode with TMP control by means of permeate distributors includes but isnot limited to a reduction in membrane fouling, a reduction in damage ofsensitive molecules, maintaining the selectivity of the membraneseparation process, and avoidance of rapid deterioration of the module.In one embodiment the conversion is set to a predetermined value bycontrolling the ratio of the feed stream flow rate to the permeatestream flow rate. In another embodiment the conversion is set to apredetermined value by controlling the ratio of the feed stream flowrate to the retentate stream flow rate. In yet another embodiment theTMP in each stage is controlled independently of the feed pressures inthe stages 2110 by using the permeate distributor 2102 to control thepermeate flow in the stages 2110.

In general, the practice of SPF uses modules made with long and thinchannels. The length can be characterized by the dimensionless length,λ, while the thickness of the channels can be characterized by thespecific membrane area of the channel, σ_(c). Mathematical modeling ofSPF processes utilizing staged modules show that the flux of an SPFmodule increases with increasing ac, thereby allowing the use of acorrespondingly smaller dimensionless channel length, λ, for a fixedconversion. This means that some SPF embodiments with sufficiently largeσ_(c) may operate with values of λ lower than about 2,000. In general,the minimum value of λ used to meet the desired conversion shows thefollowing dependence on the value of σ_(c):

$\begin{matrix}{{\lambda_{MIN} \approx \frac{B}{\sigma_{C}^{n}}};} & (12)\end{matrix}$

where the values of the parameters n and B depend on the properties ofthe solution and the desired conversion, as well as on the type ofchannel. More specifically, the value of the parameter B varies with thedesired conversion, the higher the desired conversion the higher thevalue of B.

For one example of a SPF process for concentrating BSA, utilizing stagedSPF cassettes having existing feed spacers, starting with BSAconcentrations of 5-10 g/L, and for desired conversions exceeding 80%,the values of the parameters n and B are estimated to be about 0.57 andabout 30,000, respectively, to yield the following operational formuladerived from equation 12 as follows:

$\begin{matrix}{{{\lambda > \lambda_{MIN}} = \frac{30\text{,}000}{\sigma_{C}^{0.57}}};} & (13)\end{matrix}$

where the value of σ_(c) is expressed in units of cm⁻¹. Table 4 showsthe relationship between σ_(c) and λ that results from equation 13,demonstrating that some modules having channels with a value of σ_(c)exceeding about 126 cm⁻¹ may use channels having dimensionless lengthslower than about 2000. The third column in Table 4 shows the value of aminimum channel length, L_(MIN), which decreases even faster thanλ_(MIN), demonstrating that SPF modules with channel lengths similar tothose of existing cassettes (about 18 cm) could be used to effect highconversion processes if such modules are made with channels having avalue of σ_(c) exceeding about 126 cm⁻¹.

TABLE 4 σ_(C) λ L_(MIN) [cm⁻¹] [ ] Length cm 40 3,802 95 50 3,355 67 802,579 32 100 2,276 23 126 2,000 16 300 1,230 4

Utilizing similar mathematical models, similar relationships can bederived for other applications and channel types. It is believed thatfor one set of applications, in which the target product is a proteinsimilar to BSA, the value of n ranges from about 0.3 to about 1 and thatof B ranges from approximately about 10,000 to about 1,000,000. There isno particular limit to how high σ_(c) can be, aside from possibleplugging problems associated with very small channel dimensions. If thefluids being treated are substantially free of particulate matter, σ_(c)can be very large and λ can be correspondingly lower.

It is understood that although the embodiments described herein relatespecifically to separations of interest in bio-molecular applications,the principles, practice and designs described herein are also useful inother applications. All literature and similar material cited in thisapplication, including, patents, patent applications, articles, books,treatises, dissertations and web pages, regardless of the format of suchliterature and similar materials, are expressly incorporated byreference in their entirety. In the event that one or more of theincorporated literature and similar materials differs from orcontradicts this application, including defined terms, term usage,described techniques, or the like, this application controls.

The section headings used herein are for organizational purposes onlyand are not to be construed as limiting the subject matter described inany way. While the present invention has been described in conjunctionwith various embodiments and examples, it is not intended that thepresent teachings be limited to such embodiments or examples. On thecontrary, the present invention encompasses various alternatives,modifications, and equivalents, as will be appreciated by those of skillin the art. While the teachings have been particularly shown anddescribed with reference to specific illustrative embodiments, it shouldbe understood that various changes in form and detail may be madewithout departing from the spirit and scope of the teachings. Therefore,all embodiments that come within the scope and spirit of the teachings,and equivalents thereto are claimed. The descriptions and diagrams ofthe methods of the present teachings should not be read as limited tothe described order of elements unless stated to that effect.

The claims should not be read as limited to the described order orelements unless stated to that effect. It should be understood thatvarious changes in form and detail may be made without departing fromthe scope of the appended claims. Therefore, all embodiments that comewithin the scope and spirit of the following claims and equivalentsthereto are claimed.

1. A filtration system comprising: a plurality of stages, each stagehaving a plurality of channels providing at least one serial flow path,each stage being in fluid communication with each adjacent stagepreceding it and being in fluid communication with each adjacent stagethat follows it; each of the plurality of channels comprising anfiltration membrane and having a length, a membrane area, a void volume,a specific membrane area expressed as a ratio of the membrane area tothe void volume, and a dimensionless length expressed as a product ofthe channel length and the specific membrane area; wherein adimensionless length of a stage is the sum of the dimensionless lengthsof each channel in the longest serial flow path in the stage and thedimensionless length of the system is the sum of the dimensionlesslengths of the plurality of stages; and wherein the specific membranearea of at least one channel is greater than about 40 cm⁻¹, thedimensionless length of the system is greater than about 2,000 and thedimensionless length of at least one of the plurality of stages is lessthan about 6,000.
 2. The system of claim 1 wherein an initial hydraulicpermeability of the membrane is greater than about 0.5 lmh/psi.
 3. Thesystem of claim 1 wherein the filtration membrane is one of: anultrafiltration membrane; and a microfiltration membrane.
 4. The systemof claim 1 wherein the number of stages is greater than two.
 5. Thesystem of claim 1 wherein the number of stages is greater than four. 6.The system of claim 1 wherein the channels comprise one of: a hollowfiber membrane; a flat-sheet membrane; and a membrane monolith.
 7. Thesystem of claim 1 wherein the plurality of channels in any one of theplurality of stages are substantially identical.
 8. The system of claim7 wherein the dimensionless length of each of the plurality of stages isless than about 3,500.
 9. The system of claim 7 further comprising atleast one diafiltration distributor in fluid communication with selectedones of the plurality of stages and a diafiltrate source.
 10. The systemof claim 9 wherein each of the selected ones of the plurality of stagesfurther comprises a feed manifold fluidly coupled to the channels of theselected ones of the plurality of stages and the at least onediafiltration distributor further comprises a plurality of diafiltrationflow passages fluidly coupling the feed manifolds to the diafiltratesource.
 11. The system of claim 10 further comprising a pressure sourceand wherein the diafiltrate source is supplied in the selected ones ofthe plurality of stages at a pressure greater than the feed pressure inthe channels.
 12. The system of claim 10 wherein a network of hydraulicresistances of the diafiltration flow passages of the at least onediafiltration distributor is provided as one of: a parallel arrangement;a series arrangement; and a series parallel arrangement.
 13. The systemof claim 9 further comprising: a feed manifold fluidly coupled to theplurality of channels in each stage; and at least one permeatecompartment disposed opposite at least one channel, the filtrationmembrane disposed therebetween, and wherein the at least onediafiltration flow passage fluidly couples the at least one permeatecompartment to the feed manifolds in selected preceding stages.
 14. Thesystem of claim 13 further comprising a pump disposed between the atleast one permeate compartment and the feed manifolds in selectedpreceding stages.
 15. The system of claim 7 further comprising at leastone permeate compartment disposed adjacent at least one channel of atleast one of the plurality of stages and having at least one permeatedistributor fluidly coupled to the at least one permeate compartment.16. The system of claim 7 further comprising a first stage of theplurality of stages having a greater number of channels than a secondstage of the plurality of stages following the first stage.
 17. Thesystem of claim 1 wherein the inlet width of at least one channel of atleast one of the plurality of stages is 1.2 times greater than theoutlet width of the at least one channel of at least one of theplurality of stage.
 18. The system of claim 1 further comprising atleast one change in a channel property between at least one channel of afirst stage and at least one channel of a second stage following thefirst stage.
 19. The system of claim 18 the channels of the first stageand the second stage each further comprising a feed spacer disposedadjacent the filtration membrane and wherein the property change is achange in the hydraulic diameter of the feed spacer.
 20. The system ofclaim 18 wherein the property change is at least one of: a change in thechannel cross-sectional area; a change in specific membrane area; achange in dimensionless length; a change in permeate control; and achange in the filtration membrane properties.
 21. The system of claim 20wherein the property change is monotonic between the first stage and aplurality of following stages.
 22. The system of claim 20 wherein thechange in the filtration membrane properties is at least one of: achange in membrane permeability; and a change in the molecular weightcut off of the membrane.
 23. The system of claim 1 wherein thedimensionless length of the system is greater than about 4,000 and thedimensionless length of the at least one of the plurality of stages isless than about 3,500.
 24. The system of claim 23 further comprising afirst stage having a greater number of substantially identical channelsthan a second stage following the first stage.
 25. The system of claim 1further comprising a housing and wherein the plurality of stages aredisposed within the housing.
 26. The system of claim 25 furthercomprising at least one cassette wherein the housing comprises flatplates for holding the at least one cassette.
 27. The system of claim 25wherein the housing comprises a tubular shell for holding at least onespiral-wound cartridge.
 28. The system of claim 25 wherein the housingcomprises a hollow fiber assembly.
 29. An internally staged filtrationsystem comprising: a housing; a plurality of stages disposed within thehousing, each stage having a plurality of channels comprising anfiltration membrane, each stage being in fluid communication with eachadjacent stage preceding it and being in fluid communication with eachadjacent stage that follows it, and at least two stages form a serialflow path; and wherein a filtration property of a first stage and asecond stage following the first stage differ to maintain separationperformance.
 30. The system of claim 29 further comprising at least onepermeate compartment disposed adjacent at least one channel of at leastone of the plurality of stages and having at least one permeatedistributor fluidly coupled to the at least one permeate compartment.31. The system of claim 29 wherein the filtration property is at leastone of the cross-sectional flow area of the stage; the specific membranearea of the stage; the number of channels in the stage; the hydraulicdiameter of a feed spacer disposed adjacent the membrane and within atleast one channel of a stage; and the filtration membrane properties.32. The system of claim 31 wherein the change in the cross-sectionalarea is provided by a ratio of the cross-sectional area of the firststage to the cross-sectional area of the second stage being greater thanabout 1.1.
 33. The system of claim 31 wherein the change in thecross-sectional area is provided by a ratio of the cross-sectional areaof the first stage to the cross-sectional area of the second stage beingless than about 0.8.
 34. The system of claim 31 wherein a change in themembrane properties comprises a change in the molecular weight cut offof the membrane.
 35. The system of claim 29 wherein at least one channelhas an inlet and an outlet and has a cross-sectional area whichdecreases from the inlet to the outlet.
 36. The system of claim 29wherein the specific membrane area of at least one channel is greaterthan about 40 cm⁻¹ and the dimensionless length of the system is greaterthan about 2,000 and the dimensionless length of at least one of theplurality of stages is less than about 6,000.
 37. The system of claim 29wherein the plurality of channels comprises a plurality of hollow fibermembranes; and further comprising a plurality of cylindrical flowdiverters disposed within the housing substantially parallel to thehollow fiber membranes providing a plurality of stages.
 38. The systemof claim 37 wherein the plurality of cylindrical flow diverters aredisposed to provide a different number of channels per stage.
 39. Aseparation module for the filtration of liquids comprising: a housing;and at least one hollow fiber membrane and having a hydraulicpermeability greater than about 2 lmh/psi disposed within the housingforming a flow channel, the flow channel having a membrane area, a voidvolume, a length, and the dimensionless length of the at least onehollow fiber filtration membrane is greater than about 10,000, and aspecific membrane area expressed as a ratio of the membrane area to thevoid volume wherein the specific membrane area of the at least onehollow fiber is greater than about 50 cm⁻¹.
 40. The module of claim 39wherein the specific membrane area is greater than about 80 cm⁻¹. 41.The module of claim 39 wherein the specific membrane area is greaterthan about 130 cm⁻¹.
 42. A filter module for filtering a fluid mixturecomprising: a housing; a membrane disposed within the housing having afirst surface; a feed spacer disposed adjacent the first surface of themembrane; and wherein the spacer and the membrane form at least onechannel, the at least one channel disposed to establish a tangentialflow of the fluid mixture over the first surface of the membrane and theat least one channel having a membrane area, a void volume, a length anda specific membrane area expressed as a ratio of the membrane area tothe void volume and a dimensionless length expressed as a product of thechannel length and the specific membrane area; and wherein the specificmembrane area of the at least one channel is greater than about 40 cm⁻¹,the dimensionless length of the at least one channel is greater thanabout 3,000, and the at least one channel having a width generallydecreasing in the direction of the tangential flow.
 43. The module ofclaim 42 further comprising a plurality of ribs formed adjacent the feedspacer; and wherein the decreasing width is provided by the plurality ofribs.
 44. The module of claim 43 wherein the width of the at least onechannel decreases by a factor greater than about two from an inlet ofthe channel to an outlet of the at least one channel.
 45. The module ofclaim 43 wherein the width of the at least one channel decreases by afactor greater than about 4 from an inlet of the at least one channel toan outlet of the at least one channel.
 46. The module of claim 45wherein the at least one channel has a dimensionless length greater thanabout 4,000.
 47. The module of claim 43 further comprising: a centertube disposed within the housing; a second membrane disposed oppositesaid membrane forming a spirally wound membrane element around thecenter tube; and wherein the specific membrane area is greater thanabout 50 cm⁻¹ and the width of the at least one channel decreases by afactor greater than about two from an inlet of the at least one channelto an outlet of the at least one channel.
 48. The module of claim 47wherein the width of the channel decreases by a factor greater thanabout four from an inlet of the channel to an outlet of the channel. 49.The module of claim 42 wherein the housing comprises a cassette and thespecific membrane area of the at least one channel is greater than about50 cm⁻¹ and the dimensionless length of the at least one channel isgreater than about 3,000.
 50. The cassette of claim 49 wherein thedimensionless length of the at least one channel is greater than about4,000.
 51. The cassette of claim 49 further comprising a secondfiltration membrane disposed adjacent to a second surface of the atleast one feed spacer and opposite the first filtration membrane. 52.The cassette of claim 49 wherein the feed spacer comprises aturbulence-promoting spacer.
 53. An internally staged filter modulecomprising: a housing; a plurality of stages disposed within thehousing, each stage having a plurality of channels comprising afiltration membrane and at least one manifold in fluid communicationwith the plurality of channels, each stage being in fluid communicationwith each adjacent stage preceding it and being in fluid communicationwith each adjacent stage that follows it; and at least one diafiltrationdistributor disposed within the housing and in fluid communication withthe at least one manifold of selected ones of the plurality of stagesand having an inlet for supplying a diafiltrate.
 54. The module of claim53 the at least one diafiltration distributor comprising at least onecounter current flow passage fluidly coupling the permeate from at leastone channel in a first stage as the diafiltrate to at least one channelin a selected preceding stage.
 55. The module of claim 53 wherein the atleast one diafiltration distributor further comprises a plurality ofdiafiltration flow passages fluidly coupling the feed manifolds to thediafiltrate inlet.
 56. The module of claim 55 wherein each of theplurality of diafiltration flow passages has a hydraulic resistance soas to introduce a predetermined volume of the diafiltrate into the atleast one manifold.
 57. The module of claim 56 further comprising achannel inlet fluidly coupled to an initial one of the plurality ofchannels and wherein the diafiltrate flow passage inlet pressure isabout twice the channel inlet pressure.
 58. The module of claim 55further comprising a channel inlet fluidly coupled to an initial one ofthe plurality of channels and a channel outlet fluidly coupled to a lastone of the plurality of channels, and wherein the at least onediafiltration distributor has a predetermined hydraulic resistancewherein the diafiltrate flow passage pressure is four times the averagepressure difference between the channel inlet and outlet pressure. 59.The module of claim 53 further comprising a diafiltration spacerdisposed in the at least one diafiltration flow passage providing ahydraulic resistance predetermined to control the flow rate of adiafiltrate along the at least one diafiltration flow passage.
 60. Themodule of claim 53 wherein the housing is a cylindrical housingcomprising and outer shell, an inner annular support ring and aplurality of supports coupled to the inner annular support ring; thediafiltration distributor comprises a diafiltration flow passagedisposed within the cylindrical housing and coupled to the plurality ofsupports; and the plurality of channels comprise a plurality of hollowfiber membranes disposed within housing between the outer shell and theinner annular support ring
 61. The method of claim 53 wherein thespecific membrane area of the at least one channel is greater than about40 cm⁻¹, and the dimensionless length of at least one of the pluralityof stages is less than about 3,000.
 62. A single pass filter systemcomprising: a stacked configuration comprising: a first plurality ofcassettes, each cassette having a feed manifold, a retentate manifold,at least one permeate channel, and at least one flow channel fluidlycoupled to the feed manifold and to the retentate manifold, the flowchannels of the plurality of cassettes fluidly coupled in parallel; astaging plate disposed adjacent the first plurality of cassettes; atleast one second cassette having a feed manifold and a retentatemanifold, the staging plate disposed between the first plurality ofcassettes and the at least one second cassette; and wherein the stagingplate fluidly couples the retentate manifold of one of the cassettes ofthe first plurality of cassettes to the feed manifold of the secondcassette and blocks the flow from the feed manifold of one of thecassettes of the first plurality of cassettes, thereby serializing theretentate flow through the system.
 63. The system of claim 62 furthercomprising a top plate having a feed port fluidly coupled to at leastone of the first plurality of cassettes and a bottom plate having aretentate port in fluid communication with the at least one flow channelof the at least one second cassette.
 64. The system of claim 62 whereinthe staging plate further comprises a diafiltration port in fluidcommunication with the feed manifold of one of the cassettes of thefirst plurality of cassettes.
 65. A method for filtering a liquid feedcomprising: continuously supplying the feed stream in to at a specificfeed flow rate of less than about 200 lmh into a membrane separationmodule and having at least one channel having specific membrane areagreater than about 40 cm⁻¹; and operating the separation module in asingle pass tangential flow filtration mode.
 66. The method of claim 65wherein operating the separation module in a single pass tangential flowfiltration mode further comprises controlling at least two of: the feedflow rate; the retentate flow rate; the permeate flow rate; the specificfeed rate; the transmembrane pressure (TMP) of the at least one channel;and the transchannel pressure (TCP) of the at least one channel.
 67. Themethod of claim 66 further comprising selecting a conversion factor anditeratively adjusting at least one of: the feed pressure into the atleast one channel; and a retentate pressure of the at least one channel;in response to measuring the conversion.
 68. The method of claim 66further comprising selecting a purification factor and iterativelyadjusting a diafiltration volume and at least one of: the feed pressureinto the at least one channel; and the retentate pressure of the atleast one channel; in response to measuring the purification.
 69. Themethod of claim 65 further comprising supplying the feed at a specificfeed flow rate of less than about 100 lmh.
 70. The method of claim 65further comprising controlling at least one permeate collection channelbeing at least partially formed by the filtration membrane disposedadjacent the at least one channel, having a permeate port and otherwisesealed.
 71. The method of claim 65 wherein the membrane comprises anultrafiltration membrane.
 72. The method of claim 71 further comprisingsetting the conversion to a predetermined factor by controlling theratio of the feed stream flow rate to the retentate stream flow rate.73. The method of claim 72 wherein the ratio of the feed stream flowrate to the retentate stream flow rate is provided by coupling pumps inthe feed and retentate streams.
 74. The method of claim 71 furthercomprising setting the conversion to a predetermined factor bycontrolling the ratio of the feed stream flow rate to the permeatestream flow rate.
 75. The method of claim 71 wherein the module furthercomprises a plurality of stages having a plurality of channels andfurther comprising controlling the transmembrane pressure in each stageindependently of the feed pressures in the stage by using a permeatedistributor to control the permeate flow in the stage.
 76. The method ofclaim 75 further comprising operating with a feed pressure of greaterthan about 60 psi.
 77. The method of claim 71 wherein the filtrationseparation module is at least one of: a hollow fiber cartridge; aplate-and-frame assembly, a cassette, and a spiral wound module.
 78. Themethod of claim 77 further comprising controlling the specific feed flowrate such that the average fluid residence time in the hollow fibercartridge is greater than about 20 seconds.
 79. The method of claim 77further comprising controlling the specific feed flow rate such that theaverage fluid residence time in the cassette is greater than about 2seconds.
 80. The method of claim 71 wherein the module further comprisesa plurality of stages having a plurality of channels having specificmembrane areas greater than about 40 cm⁻¹.
 81. The method of claim 71wherein the module further comprises a plurality of stages having aplurality of channels and at least one diafiltrate distributor having aplurality of diafiltration flow passages, and further comprising addinga diafiltrate through the at least one diafiltrate distributor anddistributing the diafiltrate to corresponding ones of the plurality ofchannels.
 82. The method of claim 81 further comprising supplying thediafiltrate in a selected stage, the diafiltrate source pressure greaterthan about one and one half times the feed pressure in the channel toreduce the effect of varying channel pressures on diafiltrate flow rate.83. The method of claim 81 further comprising supplying the diafiltratein a selected stage at a source pressure of about 10 psi greater thanthe feed pressure in the channel to reduce the effect of varying channelpressures on diafiltrate flow rate.
 84. The method of claim 81 furthercomprising operating the filtration separation module in a countercurrent diafiltration mode by fluidly coupling the permeate from atleast one permeate compartment as the diafiltrate to at least onepreceding channel.
 85. The method of claim 65 wherein the module is aninternally staged filtration separation module.
 86. The method of claim65 wherein the membrane comprises a microfiltration membrane.
 87. Amethod for efficiently using filtration membranes for processing asolute in a feed stream while achieving a high conversion factor andreducing system requirements, hold-up volume and processing time, themethod comprising: operating a plurality of stages, at least one stagecomprising a plurality of substantially identical, long thin channelscomprising the filtration membrane, in SPF mode; maintaining separationperformance in at least one of the plurality of stages by varying atleast one property of at least one stage relative to a preceding stage;and continuously supplying the feed stream at a specific feed flow rateof less than about 200 lmh.
 88. The method of claim 87 furthercomprising serially combining the plurality of stages to provide atleast one flow path.
 89. The method of claim 87 wherein the channels arecharacterized by having a specific membrane area greater than about 40cm⁻¹.
 90. The method of claim 89 wherein the sum of the dimensionlesslengths of the plurality of stages is greater than about 2,000.
 91. Themethod of claim 87 wherein the dimensionless length of each stage isless than about 6,000.
 92. The method of claim 87 wherein varying atleast one stage property comprises varying at least one of: the numberof channels; the cross-sectional area of the stage along the flow path;the hydraulic diameter of a spacer disposed within the channels; thespecific membrane area; and the filtration membrane properties.
 93. Themethod of claim 87 wherein the separation performance is maintained byaffecting in at least one stage at least one of: a transmembranepressure; a feed stream velocity; and a bulk concentration of thesolute.
 94. The method of claim 87 wherein continuously supplying thefeed stream further comprises operating a feed supply device to providean inlet pressure greater than about 60 psi.
 95. The method of claim 87further comprising adding a diafiltrate to the feed stream by fluidlycoupling at least one channel in the at least one stage to at least onediafiltrate flow passage.
 96. The method of claim 95 wherein varying atleast one property of the stage comprises adding diafiltrate to the atleast one stage at a predetermined rate.
 97. The method of claim 96wherein the predetermined rate is substantially equal for selected onesof the plurality of stages.
 98. The method of claim 97 furthercomprising supplying diafiltrate at a source pressure greater than thefeed pressure using a diafiltration distributor.
 99. The method of claim87 wherein maintaining separation performance further comprisescontrolling the flow of a permeate stream from at least one stage. 100.The method of claim 99 wherein controlling the flow of the permeatestream from at least one stage comprises predetermining the hydraulicresistance of a plurality of permeate flow passages of a permeatedistributor.
 101. The method of claim 87 wherein maintaining separationperformance further comprises controlling transmembrane pressure tosubstantially equalize the maximum transmembrane pressure in each of theplurality of stages.
 102. The method of claim 87 wherein maintainingseparation performance further comprises maintaining transmembranepressure in each of the plurality of stages below a value of about 40psi using at least one permeate distributor.
 103. The method of claim 87wherein the plurality of stages are disposed in at least one of: ahollow fiber cartridge; a plate-and-frame assembly, a cassette, and aspiral wound module.